Simple Harmonic Motion
181 Questions
Start JEE Mains Test
2014
Q151
JEE Mains
MCQ
10 Mar 2026
A particle moves with simple harmonic motion in a straight line. In first $\tau s,$ after starting from rest it travels a distance $a,$ and in next $\tau s$ it travels $2a,$ in same direction, then:
A.
amplitude of motion is $3a$
B.
time period of oscillations is $8\tau $
C.
amplitude of motion is $4a$
D.
time period of oscillations is $6\tau $
2013
Q152
JEE Mains
MCQ
10 Mar 2026
The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5s$. In another $10s$ it will decrease to $\alpha $ times its original magnitude, where $\alpha $ equals
A.
$0.7$
B.
$0.81$
C.
$0.729$
D.
$0.6$
2013
Q153
JEE Mains
MCQ
10 Mar 2026
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $M.$ The piston and the cylinder have equal cross sectional area $A$. When the piston is in equilibrium, the volume of the gas is ${V_0}$ and its pressure is ${P_0}.$ The piston is slightly displaced from the equilibrium position and released,. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frquency
A.
${1 \over {2\pi }}\,{{A\gamma {P_0}} \over {{V_0}M}}$
B.
${1 \over {2\pi }}\,{{{V_0}M{P_0}} \over {{A^2}\gamma }}$
C.
${1 \over {2\pi }}\,\sqrt {{{A\gamma {P_0}} \over {{V_0}M}}} $
D.
${1 \over {2\pi }}\,\sqrt {{{M{V_0}} \over {A\gamma {P_0}}}} $
2012
Q154
JEE Mains
MCQ
10 Mar 2026
If a simple pendulum has significant amplitude (up to a factor of $1/e$ of original ) only in the period between $t = 0s\,\,to\,\,t = \tau \,s,$ then $\tau \,$ may be called the average life of the pendulum When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with $b$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds :
A.
${{0.693} \over b}$
B.
$b$
C.
${1 \over b}$
D.
${2 \over b}$
2011
Q155
JEE Mains
MCQ
10 Mar 2026
Two particles are executing simple harmonic motion of the same amplitude $A$ and frequency $\omega $ along the $x$-axis. Their mean position is separated by distance ${X_0}\left( {{X_0} > A} \right)$. If the maximum separation between them is $\left( {{X_0} + A} \right),$ the phase difference between their motion is:
A.
${\pi \over 3}$
B.
${\pi \over 4}$
C.
${\pi \over 6}$
D.
${\pi \over 2}$
2011
Q156
JEE Mains
MCQ
10 Mar 2026
A mass $M,$ attached to a horizontal spring, executes $S.H.M.$ with amplitude ${A_1}.$ When the mass $M$ passes through its mean position then a smaller mass $m$ is placed over it and both of them move together with amplitude ${A_2}.$ The ratio of $\left( {{{{A_1}} \over {{A_2}}}} \right)$ is :
A.
${{M + m} \over M}$
B.
${\left( {{M \over {M + m}}} \right)^{{1 \over 2}}}$
C.
${\left( {{{M + m} \over M}} \right)^{{1 \over 2}}}$
D.
${M \over {M + m}}$
2009
Q157
JEE Mains
MCQ
10 Mar 2026
If $x,$ $v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T,$ then, which of the following does not change with time?
A.
$aT/x$
B.
$aT + 2\pi v$
C.
$aT/v$
D.
${a^2}{T^2} + 4{\pi ^2}{v^2}$
2007
Q158
JEE Mains
MCQ
10 Mar 2026
A point mass oscillates along the $x$-axis according to the law $x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).$ If the acceleration of the particle is written as $a = A\,\cos \left( {\omega t + \delta } \right),$ then
A.
$A = {x_0}{\omega ^2},\,\,\delta = 3\pi /4$
B.
$A = {x_0},\,\,\delta = - \pi /4$
C.
$A = {x_0}{\omega ^2},\,\,\delta = \pi /4$
D.
$A = {x_0}{\omega ^2},\,\,\delta = - \pi /4$
2007
Q159
JEE Mains
MCQ
10 Mar 2026
Two springs, of force constant ${k_1}$ and ${k_2}$ are connected to a mass $m$ as shown. The frequency of oscillation of the mass is $f.$ If both ${k_1}$ and ${k_2}$ are made four times their original values, the frequency of oscillation becomes
A.
$2f$
B.
$f/2$
C.
$f/4$
D.
$4f$
2007
Q160
JEE Mains
MCQ
10 Mar 2026
The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times {10^{ - 2}}$ $cos$ $\pi t$ metre. The time at which the maximum speed first occurs is
A.
$0.25$ $s$
B.
$0.5$ $s$
C.
$0.75$ $s$
D.
$0.125$ $s$
2007
Q161
JEE Mains
MCQ
10 Mar 2026
A particle of mass $m$ executes simple harmonic motion with amplitude a and frequency $v.$ The average kinetic energy during its motion from the position of equilibrium to the end is
A.
$2{\pi ^2}\,m{a^2}{v^2}$
B.
${\pi ^2}\,m{a^2}{v^2}$
C.
${1 \over 4}\,m{a^2}{v^2}$
D.
$4{\pi ^2}m{a^2}{v^2}$
2006
Q162
JEE Mains
MCQ
10 Mar 2026
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motoin of angular frequency $\omega .$ The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
A.
at the mean position of the platform
B.
for an amplitude of ${g \over {{\omega ^2}}}$
C.
For an amplitude of ${{{g^2}} \over {{\omega ^2}}}$
D.
at the height position of the platform
2006
Q163
JEE Mains
MCQ
10 Mar 2026
The maximum velocity of a particle, executing simple harmonic motion with an amplitude $7$ $mm,$ is $4.4$ $m/s.$ The period of oscillation is
A.
$0.01$ $s$
B.
$10$ $s$
C.
$0.1$ $s$
D.
$100$ $s$
2006
Q164
JEE Mains
MCQ
10 Mar 2026
Starting from the origin a body oscillates simple harmonically with a period of $2$ $s.$ After what time will its kinetic energy be $75\% $ of the total energy?
A.
${1 \over 6}s$
B.
${1 \over 4}s$
C.
${1 \over 3}s$
D.
${1 \over 12}s$
2005
Q165
JEE Mains
MCQ
10 Mar 2026
The function ${\sin ^2}\left( {\omega t} \right)$ represents
A.
a periodic, but not $SHM$ with a period ${\pi \over \omega }$
B.
a periodic, but not $SHM$ with a period ${{2\pi } \over \omega }$
C.
a $SHM$ with a period ${\pi \over \omega }$
D.
a $SHM$ with a period ${{2\pi } \over \omega }$
2005
Q166
JEE Mains
MCQ
10 Mar 2026
Two simple harmonic motions are represented by the equations ${y_1} = 0.1\,\sin \left( {100\pi t + {\pi \over 3}} \right)$ and ${y_2} = 0.1\,\cos \,\pi t.$ The phase difference of the velocity of particle $1$ with respect to the velocity of particle $2$ is
A.
${\pi \over 3}$
B.
${{ - \pi } \over 6}$
C.
${\pi \over 6}$
D.
${{ - \pi } \over 3}$
2005
Q167
JEE Mains
MCQ
10 Mar 2026
If a simple harmonic motion is represented by ${{{d^2}x} \over {d{t^2}}} + \alpha x = 0.$ its time period is
A.
${{2\pi } \over {\sqrt \alpha }}$
B.
${{2\pi } \over \alpha }$
C.
$2\pi \sqrt \alpha $
D.
$2\pi \alpha $
2005
Q168
JEE Mains
MCQ
10 Mar 2026
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
A.
first decrease and then increase to the original value
B.
first increase and then decrease to the original value
C.
increase towards a saturation value
D.
remain unchanged
2004
Q169
JEE Mains
MCQ
10 Mar 2026
A particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency ${\omega _0}.$ An external force $F(t)$ proportional to $\cos \,\omega t\left( {\omega \ne {\omega _0}} \right)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
A.
${1 \over {m\left( {\omega _0^2 + {\omega ^2}} \right)}}$
B.
${1 \over {m\left( {\omega _0^2 - {\omega ^2}} \right)}}$
C.
${m \over {\omega _0^2 - {\omega ^2}}}$
D.
${m \over {\omega _0^2 + {\omega ^2}}}$
2004
Q170
JEE Mains
MCQ
10 Mar 2026
In forced oscillation of a particle the amplitude is maximum for a frequency ${\omega _1}$ of the force while the energy is maximum for a frequency ${\omega _2}$ of the force; then
A.
${\omega _1} < {\omega _2}$ when damping is small and ${\omega _1} > {\omega _2}$ when damping is large
B.
${\omega _1} > {\omega _2}$
C.
${\omega _1} = {\omega _2}$
D.
${\omega _1} < {\omega _2}$
2004
Q171
JEE Mains
MCQ
10 Mar 2026
The bob of a simple pendulum executes simple harmonic motion in water with a period $t,$ while the period of oscillation of the bob is ${t_0}$ in air. Neglecting frictional force of water and given that the density of the bob is $\left( {4/3} \right) \times 1000\,\,kg/{m^3}.$ What relationship between $t$ and ${t_0}$ is true
A.
$t = 2{t_0}$
B.
$t = {t_0}/2$
C.
$t = {t_0}$
D.
$t = 4{t_0}$
2004
Q172
JEE Mains
MCQ
10 Mar 2026
A particle at the end of a spring executes $S.H.M$ with a period ${t_1}$. While the corresponding period for another spring is ${t_2}$. If the period of oscillation with the two springs in series is $T$ then
A.
${T^{ - 1}} = t_1^{ - 1} + t_2^{ - 1}$
B.
${T^2} = t_1^2 + t_2^2$
C.
$T = {t_1} + {t_2}$
D.
${T^{ - 2}} = t_1^{ - 2} + t_2^{ - 2}$
2004
Q173
JEE Mains
MCQ
10 Mar 2026
The total energy of particle, executing simple harmonic motion is
A.
independent of $x$
B.
$ \propto \,{x^2}$
C.
$ \propto \,x$
D.
$ \propto \,{x^{1/2}}$
2003
Q174
JEE Mains
MCQ
10 Mar 2026
A mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $SHM$ of time period $T.$ If the mass is increased by $m.$ the time period becomes ${{5T} \over 3}$. Then the ratio of ${{m} \over M}$ is
A.
${3 \over 5}$
B.
${25 \over 9}$
C.
${16 \over 9}$
D.
${5 \over 3}$
2003
Q175
JEE Mains
MCQ
10 Mar 2026
A body executes simple harmonic motion. The potential energy $(P.E),$ the kinetic energy $(K.E)$ and total energy $(T.E)$ are measured as a function of displacement $x.$ Which of the following statements is true ?
A.
$K.E$ is maximum when $x=0$
B.
$T.E$ is zero when $x=0$
C.
$K.E$ is maximum when $x$ is maximum
D.
$P.E$ is maximum when $x=0$
2003
Q176
JEE Mains
MCQ
10 Mar 2026
The displacement of particle varies according to the relation
$x=4$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$ The amplitude of the particle is
$x=4$$\left( {\cos \,\pi t + \sin \,\pi t} \right).$ The amplitude of the particle is
A.
$-4$
B.
$4$
C.
$4\sqrt 2 $
D.
$8$
2003
Q177
JEE Mains
MCQ
10 Mar 2026
Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring of spring constant ${k_1}$ and ${k_2}$, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is
A.
$\sqrt {{{{k_1}} \over {{k_2}}}} $
B.
${{{{k_2}} \over {{k_1}}}}$
C.
$\sqrt {{{{k_2}} \over {{k_1}}}} $
D.
${{{{k_1}} \over {{k_2}}}}$
2003
Q178
JEE Mains
MCQ
10 Mar 2026
The length of a simple pendulum executing simple harmonic motion is increased by $21\% $. The percentage increase in the time period of the pendulum of increased length is
A.
$11\% $
B.
$21\% $
C.
$42\% $
D.
$10\% $
2002
Q179
JEE Mains
MCQ
10 Mar 2026
In a simple harmonic oscillator, at the mean position
A.
kinetic energy is minimum, potential energy is maximum
B.
both kinetic and potential energies are maximum
C.
kinetic energy is maximum, potential energy is minimum
D.
both kinetic and potential energies are minimum.
2002
Q180
JEE Mains
MCQ
10 Mar 2026
A child swinging on a swing in sitting position, stands up, then the time period of the swing will
A.
increase
B.
decrease
C.
remains same
D.
increases of the child is long and decreases if the child is short
2002
Q181
JEE Mains
MCQ
10 Mar 2026
If a spring has time period $T,$ and is cut into $n$ equal parts, then the time period of each part will be
A.
$T\sqrt n $
B.
$T/\sqrt n $
C.
$nT$
D.
$T$