Question

A spring is mounted horizontally, with its left end fixed. A spring balance attached to the free end and pulled toward the right indicates that the stretching force is proportional to the displacement, and a force of 6.0 N causes a displacement of 0.030 m. we replace the spring balance with a 0.50 kg glider, pull it 0.020 m to the right along a frictionless air track, and release it from rest. (a) Find the force constant k of the spring. (b) find the angular frequency w, frequency f, and period T of the resulting oscillation.

Answer 1

Answer:

200 N/m

20 rad/s

0.31415 seconds

3.18309 Hz

Explanation:

m = Mass of glider = 0.5 kg

x = Displacement of spring

F = Force on spring = 6 N

From Hooke's law we have relation

$F=kx\\\Rightarrow k=\frac{F}{x}\\\Rightarrow k=\frac{6}{0.03}\\\Rightarrow k=200\ N/m$

The spring constant is 200 N/m

Angular frequency is given by

$\omega=\sqrt{\frac{k}{m}}\\\Rightarrow \omega=\sqrt{\frac{200}{0.5}}\\\Rightarrow \omega=20\ rad/s$

The angular frequency is 20 rad/s

Frequency is given by

$f=\frac{\omega}{2\pi}\\\Rightarrow f=\frac{20}{2\pi}\\\Rightarrow f=3.18309\ Hz$

The frequency is 3.18309 Hz

Time period is given by

$T=\frac{1}{f}\\\Rightarrow T=\frac{1}{3.18309}\\\Rightarrow T=0.31415\ s$

The time period is 0.31415 seconds