Question

A particle executes simple harmonic motion and is located at x = a, b and c at times t o , 2t o and 3t o respectively. The frequency of the oscillation is :

Answer 1

Hey dear,

● Answer-
f = cosinv[(a+c)/2b] / 2πt0

● Explaination-
Let,
a = Asin(wt0)
b = Acos(2wt0)
c = Acos(3wt0)

Now take,
a + c = Asin(wt0) + Asin(3wt0)
a + c = 2Asin(2wt0).cos(wt0)
a + c = 2b.cos(wt0)
cos(wt0) = (a+c)/2b

Taking inverse on both sides,
wt0 = cosinv[(a+c)/2b]
2πft0 = cosinv[(a+c)/2b]
f = cosinv[(a+c)/2b] / 2πt0

Therefore, frequency of oscillation is cosinv[(a+c)/2b] / 2πt0 .

Hope this helps you...