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A block of mass m attached to the end of a spring of spring constant ???? undergoes simple harmonic motion with amplitude ???? and angular frequency ???? . 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,????,????, and phi is increased in value. Classify which increases produce an increase in the frequency of oscillation and which do not.

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Answer:

Explanation:

Let y be the position , A be amplitude ω be angular velocity

motion of simple harmonic motion is given by the equation

y = A Cos ωt

angular frequency ω = 2π / T

It is related with mass m and spring constant k as follows

ω = [tex]\sqrt{\frac{k}{m} }[/tex]

So k increases then frequency increases , when m increases frequency decreases .

Amplitude has no effect on frequency .

Phase angle has no effect on frequency .

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