(B) The given equation for $S.H.M.$ is $y = A \sin(\omega t + \phi)$,where $A = 2 \, cm$ and $\omega = \frac{\pi}{2} \, rad/s$.The velocity $v$ is giv

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(B) The given equation for $S.H.M.$ is $y = A \sin(\omega t + \phi)$,where $A = 2 \, cm$ and $\omega = \frac{\pi}{2} \, rad/s$.The velocity $v$ is given by $\frac{dy}{dt} = A\omega \cos(\omega t + \phi)$.The acceleration $a$ is given by $\frac{d^2y}{dt^2} = -A\omega^2 \sin(\omega t + \phi)$.The maximum acceleration $a_{max}$ is given by $|A\omega^2|$.Substituting the values: $a_{max} = 2 \times \left( \frac{\pi}{2} \right)^2 = 2 \times \frac{\pi^2}{4} = \frac{\pi^2}{2} \, cm/s^2$.

Class 11 Physics Oscillations Acceleration and Force of Simple Harmonic Motion

Medium

For a particle performing $S.H.M.$ given by the equation $y = 2 \sin \left( \frac{\pi t}{2} + \phi \right) \, (cm)$,what is the maximum acceleration of the particle?

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A
$\frac{\pi}{2} \, cm/s^2$
B
$\frac{\pi^2}{2} \, cm/s^2$
C
$\frac{\pi^2}{4} \, cm/s^2$
D
$\frac{\pi}{4} \, cm/s^2$

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Oscillations

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Acceleration and Force of Simple Harmonic Motion

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For a particle performing $S.H.M.$ given by the equation $y = 2 \sin \left( \frac{\pi t}{2} + \phi \right) \, (cm)$,what is the maximum acceleration of the particle?

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Obtain instantaneous acceleration of a $SHM$ particle with the help of reference circle.

The amplitude of a particle executing $SHM$ is $2 \, cm$ and the force acting at the extreme position on the particle is $4 \, N$. What is the force at the midway point between the mean position and the extreme point (in $, N$)?

$A$ coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency $\omega$. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

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