## Find a formula for its frequency of oscillation, Mathematics

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The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is compressed a distance a and then allowed to oscillate, its displacement from its starting point is given by

f(t) = a cos√(k/mt)

a) A mass of 10g is suspended from a spring with stiffness k = 3. If the spring is compressed a distance 5 cm and then released, find the equation that describes the oscillation of the spring.

b) Find a general formula for its frequency of oscillation (in terms of k and m).

c) How is the frequency affected if the mass is increased? Is the oscillation faster or slower?

d) How is the frequency affected if a stiffer spring is used (larger k)? Is the oscillation faster or slower?

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