Question

A 0.200 kg mass attached to a horizontal spring is displaced 15.4 cm from rest and then released. If the mass oscillates 8.00 times in 19.3 s, what is the spring constant in the spring? 0.0344 N/m 1.36 N/m 6.78 N/m 0.0212 N/m

What is the time constant of an oscillator if its amplitude of oscillation is decreased to 32.3% of its original value in 8.50 s?

7.52 s 15.0 s 3.76 s 1.22 s

A ball is attached to a spring on a frictionless horizontal surface. The ball is pulled to the right and released from rest at t = 0 s. If the ball reaches a maximum speed of 28.2 cm/s and oscillates with a period of 3.00 s, what is the ball's velocity at t = 0.850 s?

-14.1 cm/s 2.81 cm/s -27.6 cm/s 3.30 cm/s

Answer 1

a)

mass, m=0.2 kg

extension, x=15.4 cm

time period, T=19.3/8 = 2.41 sec

time period ,T=2pi*sqrt(m/k)

2.41=2pi*sqrt(0.2/k)

===> k=1.36 N/m

spring constant, K=1.36 N/m

b)

if

t=8.5 sec

A=32.3% of Ao

use,

A=Ao*e^(-t/T)

0.323*Ao=Ao*e^(-8.5/T)

0.323=e^(-8.5/T)

====> T=7.52 sec

time constant, T=7.52 sec

c)

time period, T=3 sec

Vmax=28.2 cm/sec=0.282 m/sec

if t=0.85 sec

V=Vmax*cos(w*t)

v=0.282*cos((2pi/3)*0.85)

v=0.282 m/sec

or

v=2.82 cm/sec