Question

I need help with this question . Only part (d)

Answer 1

Given:

The mass of the object, m=4.85 kg

The position of the object is given by the equation,

$x=(3.75\text{ m})\cos(6.12\pi t)\text{ }\rightarrow\text{ \lparen i\rparen}$

The angular frequency, ω=19.2 rad/s

The frequency, f=3.03 Hz

The period, T=0.33 s

To find:

(d) Spring constants.

Explanation:

The spring constant of a spring is related to the angular frequency of the oscillation of the spring by the equation,

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

Where k is the spring constant.

On substituting the known values,

$\begin{gathered} 19.2=\sqrt{\frac{k}{4.85}} \\ \Rightarrow k=19.2^2\times4.85 \\ =1787.9\text{ N/m} \end{gathered}$

Final answer:

The spring constant of the spring is 1787.9 N/m