Question

An oscillating block-spring system has a mechanical energyof 1.00 J and amplitude of 10.0 cm and a maximum speed of 1.20m/s. Find (a) the spring constant and (b) the mass of theblock, and (c) the frequency of oscillation.

Answer 1

Answer:

Explanation:

Given

Mechanical Energy of Spring-Block system is 1 J

Maximum Amplitude is $A=10 cm$

maximum speed $v_{max}=1.2 m/s$

Suppose $x=A\sin \omega t$be general equation of motion of spring-mass system

where A=max amplitude

$\omega$=Natural frequency of oscillation

t=time

$v_{max}=A\omega =1.2$

$0.1\cdot \omega =1.2$

$\omega =12 rad/s$

maximum kinetic Energy must be equal to total Mechanical Energy when spring is un deformed i.e. at starting Position

$\frac{1}{2}mv_{max}^2=1$

$m=\frac{2}{1.2^2}=\frac{2}{1.44}=1.38 kg$

Also $\omega$is also given by

$\omega =\sqrt{\frac{k}{m}}$

$k=\omega ^2\cdot m$

where k= spring constant

$k=12^2\cdot 1.38$

$k=200 N/m$