Question

A 0.1-kg ball is attached to the end of an ideal spring having a force constant (spring constant) of 600 N/m.

If the spring is compressed 18 cm and released, what is the speed of the ball when it reaches a distance of 12 cm from the equilibrium position?

Determine the period.

Determine the amplitude.​

Determine the maximum speed.

Determine the total energy.

Answer 1

here,

mass , m = 0.1 kg

spring constant , K = 600 N/m

Amplitude , A = 18 cm = 0.18 m

let the speed be v1 when x1 = 0.12 m

using conservation of energy

0.5 * K * A^2 = 0.5 * K * x1^2 + 0.5 * m * v1^2

600 * 0.18^2 = 600 * 0.12^2 + 0.1 * v1^2

solving for v1

v1 = 10.4 m/s

the period , T = 2 * pi * sqrt(m/K)

T = 2 * pi * sqrt(0.1/600)

T = 0.081 s

the amplitude is 18 cm

the maximum speed , vm = A * w

vm = 0.18 * sqrt(600/0.1)

vm = 13.9 m/s

the total energy , TE = 0.5 * K * A^2

TE = 0.5 * 600 * 0.18^2 = 9.72 J