**Very Short Answer Type Questions [1 Mark Each]**

**1. **Which of the following conditions is not sufficient for SHM and why?

(a) Acceleration α displacement

(b) Restoring force α displacement

## Answer

Answer: Condition (a) is not sufficient as the direction of acceleration is opposite to displacement and that needs to be mentioned.**2. **A particle is executing SHM. Identify the positions of the particle where,

(i) K.E. of the particle is zero

(ii) P.E. is zero

(iii) P.E. is ¼ of total energy

(iv) P.E. and K.E. are equal

## Answer

Answer: (i) At both the extreme positions(ii) At mean position

**3. **How will the time period of a simple pendulum change when its length is doubled?

## Answer

Answer:**4. **Will a pendulum gain or lose time when taken to the top of a mountain?

## Answer

Answer: On the top of a mountain, acceleration due to gravity ‘g’ decreases.Time period increases. So it loses time.

**5. **Why a point on a rotating wheel cannot be considered as executing SHM?

## Answer

Answer: It is not a to-and-fro motion about a fixed point. So, it is only periodic but not oscillatory.**6. **A spring of force constant *k *is broken into *n *equal parts (*n *> 0). What will be the spring factor of each part?

## Answer

Answer: The spring factor of each part is nk.**7. **Two clocks, one working with oscillating pendulum and the other with spring are given. Which one will give correct time in a satellite?

## Answer

Answer:**8. **How would the period of a spring mass system change when it is made to oscillate horizontally and then vertically?

## Answer

Answer: Time period of a spring is independent of ‘g’. So, no change will take place.**9. **Two simple pendulum of equal lengths cross each other from opposite directions at mean position. What is their phase difference?

## Answer

Answer: π radian**10. **When is the tension maximum in the spring of a simple pendulum?

## Answer

Answer: At the mean position.11. In the arrangement, if the block of mass *m *is displaced, what is the frequency of oscillation?

## Answer

Answer: Since restoring force is equal on both the springs, frequency of the system**12. **Two identical springs of springs constant *k *are attached to a block of mass *m *and to fixed supports as shown in Fig. When the mass is displaced from equilibrium position by a distance *x *towards right, find the restoring force.

## Answer

Answer: 2kx towards left.**13. **Show that for a particle executing S.H.M. velocity and displacement have a phase difference of π/2.

## Answer

Answer: We have, x = a sinωtv = dx/dt = aω cosωt = aω sin(ωt+π/2)

Thus, there is a phase difference of π/2 between particle displacement and velocity.

**14. **What is the ratio of maximum acceleration to the maximum velocity of a simple harmonic oscillator?

## Answer

Answer: amax. / vmax. = aω2 / aω = ω**15. **A grandfather clock depends on the period of a pendulum to keep correct time. Suppose a grandfather clock is calibrated correctly and then a mischievous child slides the bob of the pendulum downward on the oscillating rod. Does the grandfather clock run (a) slow, (b) fast, or (c) correctly?

## Answer

Answer: With a longer length, the period of the pendulum increases. Thus, it takes longer to execute each swing, so that each second according to the clock takes longer than an actual second. Thus, the clock runs slow.**16. **What are the two basic characteristics of a simple harmonic motion?

## Answer

Answer: (a) Acceleration is directly proportional to displacement. (b) Acceleration is directed opposite to displacement.**17. **When will the motion of a simple pendulum be simple harmonic?