Question

Damping is negligible for a 0.155-kg object hanging from a light, 6.30-N/m spring. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.460 m?

Lower frequency--? (in Hz)

Higher frequency-- ? (in Hz)

Answer 1

Given data:

Mass of the object = 0.155 kg

Force constant of the spring = 6.30 N/m

Maximum amplitude of driving force = 1.70 N

Amplitude = 0.460 m

Damping constant = 0

The amplitude (A) of a driven oscillator is given by formula:

Where is the maximum driving force

m is the mass of the object

is the angular frequency

is the natural frequency

b is the damping constant

As damping constant is negligible. Therefore above equation becomes:

Now solving for angular frequency :

Now as natural frequency is given by:

Where k is the force constant

m is the mass of the object

Therefore our final equation becomes:

Now as frequency of oscillation is given by formula:

From equation - 1 we get:

Now substituting the values we get:

The answer is rounded to two significant figures.

Therefore, Lower frequency is 0.65 Hz

and Higher frequency is 1.3 Hz

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