Question

A 0.5 Kg mass is supported by a spring . The system is set in vibration at its natural frequency of 4 Hz with an amplitude of 5 Cm.Find the spring constant .

Answer 1

Use the formula for natural frequency f:

f = [1/(2 pi)]*sqrt(k/m)

Rearrange it to solve for the spring constant k, knowing frequency (f) and mass (m).

4 pi^2 * f^2 * m = k

The amplitude does not matter in this case. The units of the answer (k) will be Newtons per meter if f is in Hz and m is in kg, since

kg * s^-2 = (kg*m/s^2)/m = N/m

Answer 2

I had already used the above formula and calculated k = 315.8 N/m
But the book answer is k = 101 N/m
Hence this query

Answer 3

The book answer appears to be wrong by a factor of pi

Answer 4

Thanks a lot