Question

A 2.3 kg block executes SHM while attached to a horizontal spring of spring constant 150 N/m. The maximum speed of the block as it slides on a horizontal frictionless surface is 2.3 m/s. What are (a) the amplitude of the block's motion, (b) the magnitude of its maximum acceleration, and (c) the magnitude of its minimum acceleration? (d) How long does the block take to complete 4.1 cycles of its motion?

Answer 1

given,

mass of block = m = 2.3 Kg

spring constant = k = 150 N/m

speed = 2.3 m/s

a) we know,

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

`\omega = \sqrt{(150)/(2.3)}`

ω = 8.08 rad/s

v = A ω

2.3 = A x 8.08

A = 0.285 m

b) maximum acceleration

a = A ω²

a = 0.285 x 8.08²

a = 18.58 m/s²

c) acceleration is minimum at mean position the minimum value of acceleration is zero.

d) time period

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

`T = (2\pi)/(8.08)`

T = 0.778 s

t = 4.1 x 0.7778

t = 3.188 s