A block of mass m attached to the end of a spring of spring constant k undergoes simple harmonic motion with amplitude A and angular frequency ω. The position of the block is described by a cosine function with an initial phase angle ϕ = 0. Which of the variables m, k, A, or ϕ should you increase if you want to increase the frequency of oscillation?

To increase the frequency the spring constant k should be increased.

Explanation:

In simple harmonic motion, the frequency is expressed as;

f = (1/2π)√(k/m)

where;

k is spring constant

m is mass of the object

From the frequency formula i wrote, It’s obvious that frequency depends on only the spring constant and mass while Amplitude(A) and phase angle(ϕ) are not related and would have no effect on the frequency. Thus, by inspection, an increase in spring constant increases frequency while an increase in mass decreases frequency

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