The time period of a particle in SHM does not depend upon its:

Question

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Answer 1

$x = A s i n (ω t + θ)$
$\frac{d ^{2} x}{d t ^{2}} = a = - ω^{2} x$
According to Hooke's Law
$F = - k x$
$m a = - k x$
$m (- ω^{2} x) = - k x$
$ω = \frac{k}{m}$
Now, $ω = \frac{2 π}{T}$
where T is time periond. Therefore,
$T = 2 π \frac{m}{k}$ . It does not depend on acceleration and amplitude. It does depends on frequency as $T = \frac{1}{f}$ where $f$ is frequency.

Answer 2

x = A s i n (ω t + θ)

\frac{d ^{2} x}{d t ^{2}} = a = - ω^{2} x

According to Hooke's Law

F = - k x

m a = - k x

m (- ω^{2} x) = - k x

ω = \frac{k}{m}

Now,

ω = \frac{2 π}{T}

where T is time periond. Therefore,

T = 2 π \frac{m}{k}

. It does not depend on acceleration and amplitude. It does depends on frequency as

T = \frac{1}{f}

where

f

is frequency.