Question

A 130 g block attached to a spring with spring constant 3.0 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x0 = -4.0 cm .

What is the block's maximum acceleration?

What is the speed of the block when x1 = 3.2 cm ?

Answer 1

here,

mass of block , m1 = 130 g = 0.13 kg

spring constant , K = 3 N/m

x1 = - 4 cm = - 0.04 m and v1 = 20 cm = 0.2 m/s

let the amplitude of motion be A

using conservation of energy

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

0.5 * 3 * 0.04^2 + 0.5 * 0.13 * 0.2^2 = 0.5 * 3 * A^2

A = 0.058 m

the maximum accelration , am = K * A /m

am = 3 * 0.058 /0.13 m/s^2

am = 1.33 m/s^2

for x2 = 3.2 cm = 0.032 m

let the speed of the block be v2

using conservation of energy

0.5 * K * A^2 = 0.5 * m * v2^2 + 0.5 * K * x2^2

3 * 0.058^2 = 0.13 * v2^2 + 3 * 0.032^2

solving for v2

v2 = 0.054 m/s = 5.4 cm/s