1.

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm, (c) 0 cm.

Answer»

Given: amplitude (r) = 5 cm, period(t) = 0.2 sec

To find acceleration and velocity at displacement, '5' cm, '3' cm and '0' cm

(a) v = 2π/t √{(r2 - y2)} = 2π/t √{(5)2 - (5)2} = 0 ms-1

Acceleration = (2π/t)2y

= {-4π2}/{0.2 x 0.2} x 5 = -5π2 ms-2

(b) Velocity (v) = 2π/t √{(5)2 - (3)2}

= 2π/t √{(25) - (9)} = 2π/t x 4 cms-1

= 2π/0.2 x 4/100 ms-1 = 0.4π ms-1

Acceleration (a) = -(2π/t)2y

= {-4π2}/{0.2 x 0.2} x {3}/{100} ms-2

= -3π2 - ms-2

(c) Velocity (v) = 2π/t √{(5)2 - (0)2}

= 2π/t x 5 = {2π x 5 x 10}/{2 x 100} ms-1

= π/2 ms-1 = 0.5 π ms-1

Acceleration (a) = -(2π/t)2 x y

{-4π2 x 0}/{t2} = 0 ms-2


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