Oscillations - Result Question 57

62. A simple harmonic oscillator has an amplitude A and time period T. The time required by it to travel from x=A to x=A/2 is

[1992]

(a) T/6

(b) T/4

(c) T/3

(d) T/2

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Solution:

  1. (a) For S.H.M., x=Asin(2πTt)

When x=A,A=Asin(2πT.t)

sin(2πTt)=1

sin(2πTt)=sin(π2)t=(T/4)

When x=A2,A2=Asin(2πT.t)

or, sinπ6=sin(2πTt) or t=(T/12)

Now, time taken to travel from x=A to x=A/2 is (T/4T/12)=T/6



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