Question

If a mass of 0.5 kg is displaced by 30 cm using a spring with a spring constant of 2 N/m, find the following:a) The angular frequencyb) The period of oscillationc) The position at t = 2 secondsd) The velocity at t = 2 secondse) The acceleration at t = 2 seconds

Answer 1

given,

mass of the block, m = 0.5 Kg

displacement, x = 30 cm = 0.3 m

Spring constant, k = 2 N/m

a) Angular frequency

`\omega = \sqrt{(k)/(m)}`

`\omega = \sqrt{(2)/(0.5)}`

`\omega = 2\ rad/s`

b) Period of oscillation

`T=(2\pi)/(\omega)`

`T=(2\pi)/(2)`

T = 3.14 s

c) Position at t = 2

x = -A cos ω t

A = 0.3 ω = 2 rad/s

x = -0.3 cos (2 x 2)

x = 0.196 m

d) velocity at t= 2

v = A ω sin ω t

v = 0.3 x 2 x sin 4

v = -0.454 m/s

e) acceleration at t= 2

a = A ω² cos ω t

a = 0.3 x 2² cos 4

a = -0.784 m/s²