Question

2.- If a mass is vibrating at a frequency of 0.9 Hz and experiences a speed of 0.05 m / s when passing through the center of oscillation. What is its amplitude? What is the period of oscillation?

Answer 1

Let us suppose the motion to be simple harmonic.

Now, the equarion of motion is

x = A ...............(1)

Differentiating this gives

v = A .............(2)

Where the symbols,

V - velocity of the mass

X - displacement

Omega () - angular frequency ( )

t - time

- phase

A - Amplitude

According to the data,

The mass experiences a velocity of 0.05m/s when passing through the centre of osscilation. Suppose the mass starts from the centre of oscillation, with a velocity 0.05m/s and oscillates with the frequency 0.9Hz.

So, for this case equation (2) changes into

Putting the values,

A = 0.05m/s ÷ (2× 3.14 ×0.9Hz)

A = 0.009m

For the period....

T = 1÷f

(where, f is the frequency)

T = 1.11 seconds.