Question

A mass M is suspended from a spring and oscillates with a period of 0.840 s. Each complete oscillation results in an amplitude reduction of a factor of 0.96 due to a small velocity dependent frictional effect.
Calculate the time it takes for the total energy of the oscillator to decrease to 0.50 of its initial value (The amplitude after N oscillations=(initial amplitude)x(factor)^N).

Answer 1

The time it takes for the total energy of the oscillator to decrease to 0.50 of its initial value

t= 14.448 s

This is further explained below.

What is an oscillator?

An electronic oscillator is a circuit that generates a periodic, oscillating electronic signal. This signal is often a sine wave, but it may also be a square wave or a triangle wave. Oscillators are devices that change the direct current that is supplied by a power source into an alternating current signal.

Generally, the equation for amplitude  is  mathematically given as

$A_n = A_0(0.96)^n$

equal to the half-energy amplitude

$A_0(0.96)^n =\frac{ A_0}{\sqrt{2}}$

$lnA_0(0.96)^n = ln\frac{Ao}{\sqrt{2}}$

$ln(A_0)+n*ln(0.98) = ln(A_0)-ln(\sqrt{2})$

n = 17.2

In conclusion, the time is

t = nT

t= 14.448 s

Read more about oscillators

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