Question

A spring stretches by 0.0190 m when a 3.36-kg object is suspended from its end. How much mass should be attached to this spring so that its frequency of vibration is f = 3.0 Hz?

Answer 1

m = 4.87 kg

Step-by-step explanation:

In order to find the required mass you first calculate the spring constant of the spring. When the system reaches the equilibrium you obtain the following equation:

`Mg=kx` (1)

That is, the weight of the object is equal to the restoring force of the spring.

M: mass of the object = 3.36 kg

g: gravitational constant = 9.8m/s^2

k: spring constant = ?

x: elongation of the spring = 0.0190m

You solve the equation (1) for k:

`k=(Mg)/(x)=((3.36kg)(9.8m/s^2))/(0.0190m)=1733.05(N)/(m)`

Next, to obtain a frequency of 3.0Hz you can use the following formula, in order to calculate the required mass:

`f=(1)/(2\pi)\sqrt{(k)/(m)}` (2)

You solve the equation (2) for m:

`m=(1)/(4\pi^2)(k)/(f^2)\\\\m=(1)/(4\pi^2)(1733.05N/m)/((3.0Hz)^2)=4.87kg`

The required mass to obtain a frequency of 3.0Hz is 4.87 kg