An oscillator consists of a block of mass 0.500 kg connected to a spring. when set into oscillation with amplitude 47.0 cm, it is observed to repeat its motion every 0.550 s. (a) find the period. s (b) find the frequency. hz (c) find the angular frequency. rad/s (d) find the spring constant. n/m (e) find the maximum speed. m/s (f) find the maximum force exerted on the block. n

a)

b)

c)

d)

e)

f)

Explanation:

Part a

For this case we know that the mass repeat its motion every 0.550 s. And that's the definition of period so for this case

Part b

By definition the frecuency is the inverse of the period so we have this:

Part c

The angular fecuency is defined with the following formula:

And since we have the frequency we can replace:

Part d

For this case we know that the period is given by:

And if we solve for k we have this:

And since we can rewrite this expression like this:

Part e

The maximum speed for an oscillator is given by this formula:

Part f

The maximum force is given by this formula:

And the because the acceleration is the derivate of the velocity, so then we have:

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