The amplitude of an oscillator decreases to 36.7% of its initial value in 29.5 s .part a what is the value of the time constant

Given that the amplitude of an oscillator decreases to 36.7% of its initial value in 29.5 s, we want to get the time constant. We will get:

k = 0.041 s^-1

We can write a really simple oscillation equation as:

f(t) = A*cos(k*t)

Where A is the amplitude and k is the time constant.

We know that the amplitude decreases to 36.7% of its initial value to 29.5 seconds, this means that:

f(29.5s) = 0.367*A = A*cos(k*29.5s)

Dividing both sides by A, we get:

0.367 = cos(k*29.5s)

So we just need to solve the above equation for k.

If we use the inverse cosine function in both sides, we get:

Acos(0.367) = Acos(cos(k*29.5s))

Acos(0.367) = k*29.5s

1.195 = k*29.5s

1.195/29.5s = k = 0.041 s^-1

The time constant is:

k = 0.041 s^-1

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