Ablock of mass m attached to the end of a spring of spring constant undergoes simple harmonic motion with amplitude and angular frequency ω. the position of the block is described by a cosine function with an initial phase angle phi=0 . suppose that each of the variables m, k,a, and ϕ is increased in value. classify which increases produce an increase in the frequency of oscillation and which do not. increases frequency does not increase frequency.
options:
increase a
increase k
increase m
increase phi

Increase in A- No effect

Increase in K- Increases frequency

Increase in m- decreases frequency

increase in phi- no effect

Explanation:

The frequency of oscillation is given by

where k is spring constant, m is mass of the object

It’s clear that frequency depends on spring constant and mass. Therefore, an increase in spring constant increases frequency and an increase in mass decreases frequency

Both an increase in amplitude and will have no effect on the frequency since they are not co-related

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