An object on the end of a spring with spring constant k moves in simple harmonic motion with amplitude a and frequency f. which of th following is a possible expression for the kinetic energy of the object as a function of time t? (a) ka2 sin2 (2tft) (b) aka cos (2t ft) (c) ka sin (2n ft) (d) ka cos (2tt ft)

Explanation:

It is given that, an object on the end of a spring with spring constant k moves in simple harmonic motion with amplitude A and frequency f.

The equation of a particle executing SHM is given by :

.........(1)

Where

A is the amplitude of the wave

Differentiating equation (1) wrt t as :

.........(2)

The kinetic energy of the particle is given by :

.........(3)

We know that,

So, equation (3) becomes :

or

So, the kinetic energy of the object is . Hence, this is the required solution.

(75°f − 32) × 5/9 = 23.889°c

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