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horsena [70]
3 years ago
14

a mass spring system makes 50 complete osillations in 10 seconds. what is the period and frequency of the oscillations

Physics
1 answer:
Oxana [17]3 years ago
5 0

Answer: Period = 0.2 seconds; frequency = 5Hz

Explanation:

Number of oscillations = 50

Time required = 10 seconds

Period (T) = ?

Frequency of the oscillations (F) = ?

A) Recall that frequency is the number of oscillations that the mass spring system completes in one second.

i.e Frequency = (Number of oscillations / time taken)

F = 50/10 = 5Hz

B) Period, T is inversely proportional to frequency. i.e Period = 1/Frequency

T = 1/5Hz

T = 0.2 seconds

Thus, the the period and frequency of the oscillations are 0.2 seconds and 5Hz respectively.

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\alpha_a = \frac{\Delta \omega}{\Delta t} = \frac{12.57}{10} = 1.257 rad/s^2

The angular acceleration when it stopping:

\alpha_o = \frac{\Delta \omega}{\Delta t} = \frac{-12.57}{12} = -1.05 rad/s^2

The angular distance it covers when starting from rest:

\omega^2 - 0^2 = 2\alpha_a\theta_a

\theta_a = \frac{\omega^2}{2\alpha_a} = \frac{12.57^2}{2*1.257} = 62.8 rad

The angular distance it covers when coming to complete stop:

0 - \omega^2 = 2\alpha_o\theta_o

\theta_o = \frac{-\omega^2}{2\alpha_o} = \frac{-12.57^2}{2*(-1.05)} = 75.4 rad

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