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SHM expression

Out of the fo...

Question

Out of the following functions representing motion of a particle which represent S.H.M?
$I . y = s i n ω t - c o s ω t$
$I I . y = s i n^{3} ω t$
$I I I . y = 5 c o s (\frac{3 π}{4} - 3 ω t)$
$I V . y = 1 + ω^{2} t^{2} + ω t$

Only

(I V)

does not represent S.H.M.

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(I)

and

(I I I)

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(I)

and

(I I)

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Only

(I)

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Solution

The correct option is B $(I)$ and $(I I I)$
Simple harmonic motions are periodic motions whose displacements can be represented as the linear sum of $s i n$ and $c o s$ functions.

Only $I$ and $I I I$ satisfy the criteria.

Suggest Corrections

Similar questions

I . y = s i n ω t - c o s ω t

I I . y = s i n^{3} ω t

I I I . y = 5 c o s (\frac{3 π}{4} - 3 ω t)

I V . y = 1 + ω^{2} t^{2} + ω t

S H M

y = sin ω t - cos ω t

y = {sin}^{3} ω t

y = 5 cos (\frac{3 π}{4} - 3 ω t)

y = 1 + ω t + ω^{2} t^{2}

I . y = s i n ω t - c o s ω t

I I . y = s i n^{3} ω t

I I I . y = 5 c o s (\frac{3 π}{4} - 3 ω t)

I V . y = 1 + ω^{2} t^{2} + ω t

x = s i n^{3} ω t

x = 1 + ω t + ω^{2} t^{2}

x = c o s ω t + c o s 3 ω t + c o s 5 ω t

x = s i n ω t + c o s ω t

y = {sin}^{3} ω t

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