Question

a 350g mass as attached to a spring of constant 5.2N/m and set into oscillation with amplitude of 10 cm. what is the frequency, period, maximum velocity and the maximum force in the spring?

Answer 1

Explanation:

It is given that,

Mass of the object, m = 350 g = 0.35 kg

Spring constant of the spring, k = 5.2 N/m

Amplitude of the oscillation, A = 10 cm = 0.1 m

Frequency of a spring mass system is given by :

$f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}} \\\\f=\dfrac{1}{2\pi}\sqrt{\dfrac{5.2}{0.35}} \\\\f=0.613\ Hz$

Time period:

$T=\dfrac{1}{f}\\\\T=\dfrac{1}{0.613}\\\\T=1.63\ s$

Maximum velocity in the spring is given by :

$v=A\omega$

$v=A\sqrt{\dfrac{k}{m}} \\\\v=0.1\times \sqrt{\dfrac{5.2}{0.35}} \\\\v=0.38\ m/s$

The maximum force acting in the spring is :

$F=-kx\\\\F=kA\\\\F=5.2\times 0.1\\\\F=0.52\ N$

Hence, this is the required solution.