Unit – 10 : Oscillations (Multiple Choice Questions)

1. In simple harmonic motion, the acceleration against displacement for one complete oscillation will be

a) an ellipse
b) a circle
c) a parabola
d) a straight line
Answer: d)

2. A particle executing SHM crosses points A and B with same velocity. Having taken 3 s in passing from A to B, it returns to B after another 3 s. The time period is

a) 15 s
b) 6 s
c) 12 s
d) 9 s
Answer: c)

3. The length of a seconds pendulum on Earth is 0.9 m. The length of the same pendulum on a planet X where acceleration due to gravity is $n$ times that of Earth is

a) $0.9n$
b) $\dfrac{0.9}{n}$
c) $0.9n^2$
d) $\dfrac{0.9}{n^2}$
Answer: a)

4. A simple pendulum is suspended from the roof of a bus moving horizontally with acceleration $a$. The time period is

a) $T_0=\dfrac{1}{\sqrt{g^2+a^2}}$
b) $T_0\sqrt{\dfrac{1}{g^2+a^2}}$
c) $T_0\sqrt{g^2+a^2}$
d) $T_0(g^2+a^2)$
Answer: b)

5. Two bodies A and B of masses in ratio 1:2 are suspended from springs of force constants $k_A$ and $k_B$. If their maximum velocities are in ratio 1:2, the ratio of amplitudes is

a) $\sqrt{\dfrac{k_B}{2k_A}}$
b) $\sqrt{\dfrac{k_B}{8k_A}}$
c) $\sqrt{\dfrac{2k_B}{k_A}}$
d) $\sqrt{\dfrac{8k_B}{k_A}}$
Answer: b)

6. A spring connected to mass $m$ has time period $T$. If the spring is cut into two equal halves and same mass is suspended, the new period is

a) $T'=\sqrt{2}T$
b) $T'=\dfrac{T}{\sqrt{2}}$
c) $T'=2T$
d) $T'=\sqrt{\dfrac{T}{2}}$
Answer: b)

7. The displacement of SHM is $y(t)=A\sin(\omega t+\phi)$. Given $A=8$ cm, $T=24$ s and $y(0)=4$ cm. The displacement at $t=6$ s is

a) 8 cm
b) 4 cm
c) $4\sqrt{3}$ cm
d) $8\sqrt{3}$ cm
Answer: d)

8. A simple pendulum has time period $T_1$. If the point of suspension moves vertically upward as $y=kt^2$, where $k=1\,m\,s^{-2}$, then $\dfrac{T_1^2}{T_2^2}$ is

a) $\dfrac{5}{6}$
b) $\dfrac{11}{10}$
c) $\dfrac{6}{5}$
d) $\dfrac{5}{4}$
Answer: c)

9. A spring of constant $k$ has mass $M$ attached. If released from unstretched position, the maximum extension is

a) $\dfrac{4Mg}{k}$
b) $\dfrac{Mg}{k}$
c) $\dfrac{2Mg}{k}$
d) $\dfrac{Mg}{2k}$
Answer: c)

10. A pendulum oscillates freely in a high building. If acceleration at 4 m from mean position is $16\,ms^{-2}$, the time period is

a) 2 s
b) 1 s
c) $2\pi s$
d) $\pi s$
Answer: d)

11. A hollow sphere filled with water is hung by a thread. As water flows out, the period of oscillation

a) first increases then decreases
b) first decreases then increases
c) increases continuously
d) decreases continuously
Answer: a)

12. The damping force on an oscillator is proportional to velocity. The unit of proportionality constant is

a) kg m s$^{-1}$
b) kg m s$^{-2}$
c) kg s$^{-1}$
d) kg s
Answer: c)

13. The total energy of SHM with $\omega=1\,rad\,s^{-1}$ is 0.256 J. If displacement at $t=\dfrac{\pi}{2}$ s is $8\sqrt{2}$ cm, the amplitude is

a) 8 cm
b) 16 cm
c) 32 cm
d) 64 cm
Answer: b)

14. A particle executes SHM. Displacements at times $t_0$, $2t_0$ and $3t_0$ are A, B and C respectively. Then $\dfrac{A+C}{2B}$ equals

a) $\cos \omega t_0$
b) $\cos 2\omega t_0$
c) $\cos 3\omega t_0$
d) 1
Answer: a)

15. A mass of 3 kg is attached to a spring executing SHM with amplitude 2 m and time period $2\pi$. The maximum force exerted is

a) 1.5 N
b) 3 N
c) 6 N
d) 12 N
Answer: c)