Question

Maximum acceleration of a particle in SHM is 16 cm//s^(2) and maximum uelocity is 8 cm//s.Find time period and amplitude of oscillations.

Answer 1

Time period of SHM is 2s

Amplitude of SHM is 4 units

• A motion which is periodic , oscillatary & can be expressed with harmonic function is simple harmonic motion.

•Generally , displacement function of particle doing SHM is given by ,

x = Asin wt

•On differentiating with respect to time

V = A√(A²-x²)

Now , V will be max. at x = 0

so , Vmax = wA ______(2)

•On differentiating V we get ,

a = -w²A sin wt

Now , a will be maximum when

sin wt = 1

so, a (max) = -w²A _____(3)

• On dividing (2) from (3)

we get , a(max) / Vmax = w

w = 16/8

w = 2s

Time period of SHM is 2s

•also wA = Vmax

(2)A = 8

A = 4

Amplitude of SHM is 4 units