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

Step-by-step 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=(1)/(2\pi)\sqrt{(k)/(m)} \\\\f=(1)/(2\pi)\sqrt{(5.2)/(0.35)} \\\\f=0.613\ Hz`

Time period:

`T=(1)/(f)\\\\T=(1)/(0.613)\\\\T=1.63\ s`

Maximum velocity in the spring is given by :

`v=A\omega`

`v=A\sqrt{(k)/(m)} \\\\v=0.1* \sqrt{(5.2)/(0.35)} \\\\v=0.38\ m/s`

The maximum force acting in the spring is :

`F=-kx\\\\F=kA\\\\F=5.2* 0.1\\\\F=0.52\ N`

Hence, this is the required solution.