CHAPTER 7 OSCILLATIONS

 

7.1      Multiple choice questions.

1.      The acceleration of a body in simple harmonic motion is
(a) Zero at each point	(b) Remain same at each point
(c) Maximum at mean position	(d) Maximum at extreme position
2.      What is the value of a spring constant when a 100 g mass is connected with a spring and it is accelerated 0.5 ms-2 through a displacement of 5cm?
(a) 0.1 N m-1	(b) 0.5 N m-1
(c) 1 N m-1	(d) 5 N m-1
3.      If a spring of forced constant K is cut into two equal parts. Then the spring constant of each half is
(a) k/2	(b) 2k
(c) k	(d) k/ √2
4.      When a body is performing S.H.M then at its extreme position.
(a) Displacement is zero	(b) Amplitude is zero
(c) Velocity is a zero	(d) P.E is zero
5.      A particle is executing S.H.M along a straight line with amplitude A. Its kinetic energy is maximum when its displacement is
(a) ±A	(b) ±A/2
(c) Zero	(d) ±A/√2
6.      The time period of a body attached to a spring depends upon
(a) Amplitude	(b) Mass
(c) Length	(d) Displacement
7.      When the length of the pendulum is increased four times then its time period is increased
(a) One time	(b) Two time
(c) Three time	(d) Four time
8.      What is the frequency of the body when its time period is 2 seconds?
(a) 1 Hz	(b) 2 Hz
(c) 0.2 Hz	(d) 0.5 Hz
9.      A second’s pendulum is one who has a time period of
(a) 1 s	(b) 2 s
(c) 1/2 s	(d) 0.2 s
10.  In S.H.M at what distance from mean position in terms amplitude x0, where K.E and P.E have equal value?
(a) 0.51x0	(b) 0.61x0
(c) 0.71x0	(d) 0.81x0
11.  The instantaneous K.E of a mass attached to the end of an elastic spring is
(a) k(x20 - x2)	(b) k(x20 + x2)
(c) k(x2 - x20 )	(d) k(x - x0 )
12.  In S.H.M., we have the conservation of
(a) Kinetic energy	(b) Potential energy
(c) Total energy	(d) Mechanical energy
13.  A free oscillation has constant
(a) Energy	(b) Amplitude
(c) Frequency	(d) All of these
14.  When damping force is equal to the force oscillation then the damping is called.
(a) Under damping	(b) Critical damping
(c) Over damping	(d) No damping
15.  A resonance is occurred when driving frequency is
(a) Less than the natural frequency	(b) Greater than natural frequency
(c) Equal to the natural frequency	(d) Equal to zero
16.  In the absence of damping force, when driving frequency is equal to Oscillating frequency then the amplitude of the oscillation will become
(a) Zero	(b) Minimum
(c) Maximum	(d) Infinity
17.  Food is cooked in a microwave oven by the effect of
(a) Interference	(b) Mechanical resonance
(c) Magnetic resonance	(d) Electric resonance

 

Answers

1. (c) Maximum at mean position
2. (c) 1 N m^-1
3. (b) 2k
4. (c) Velocity is a zero
5. (c) Zero
6. (b) Mass
7. (b) Two time
8. (d) 0.5 Hz
9. (b) 2 s
10. (c) 0.71x₀
11. (a) k(x²₀ - x²)
12. (d) Mechanical energy
13. (c) Frequency
14. (b) Critical damping
15. (c) Equal to the natural frequency
16. (c) Maximum
17. (c) Magnetic resonance

7.2      Short questions

7. Show that in S.H.M the acceleration is zero when the velocity is maximum, and the velocity is zero when the acceleration is maximum.

15. What happens to the period of a simple pendulum if its length is doubled?

7.3      Numerical problems

1. When a 600 g of mass is suspended at the end of a vertical spring and the spring f stretches 0.45 m. What is the spring constant of the spring and how much further will Stretch? If an additional mass of 600 g is hung from it.

2. A 2 kg mass is executing S.H.M and makes 4 vibrations per second. Calculates the acceleration and the restoring force acting in the body when its displacement from mean position is 7 cm.

6. How much time period of a simple pendulum is increased by increasing it length from 0.8 m to 0.993 m?

8. A car of mass 1300 kg is constructed using a frame supported by four spring each spring has a spring constant 20000 Nm^-1. If two people riding in the car have a combined mass of 160 kg, find the frequency of vibration of the Car. When it is driven over a pot-hole in the road. Assume the weight is evenly disturbed.