Q6 of 31 Page 358

Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

(a) a = 0.7x


(b) a = –200x2


(c) a = –10x


(d) a = 100x3

The relation between displacement and acceleration involves S.H.M when acceleration is proportional to displacement and is directed in the opposite direction.

In (c) acceleration is proportional to displacement x and directed in the opposite direction. Hence, only (c) a = –10x involves Simple Harmonic motion.


More from this chapter

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4

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (ω is any positive constant):

(a) sin ωt – cos ωt


(b) sin3 ωt


(c) 3 cos (π/4 – 2ωt)


(d) cos ωt + cos 3ωt + cos 5ωt


(e) exp (–ω2t2)


(f) 1 + ωt + ω2t2

5

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is

(a) at the end A,


(b) at the end B,


(c) at the mid-point of AB going towards A,


(d) at 2 cm away from B going towards A,


(e) at 3 cm away from A going towards B, and


(f) at 4 cm away from B going towards A.

 7

The motion of a particle executing simple harmonic motion is described by the displacement function,

x(t) = A cos (ωt + φ).


If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle? The angular frequency of the particle is π s–1. If instead of the cosine function, we choose the sine function to describe the SHM x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.

8

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?