IAT (IISER) 2024 | Simple Harmonic Motion Question 1 | Physics

Consider a simple pendulum undergoing simple harmonic motion with a time period $T$, and a fixed amplitude $\theta_0$ of angular oscillation. Its angular momentum about the point of suspension exhibits an oscillatory behaviour with an amplitude $A$. Which of the following relations between $A$ and $T$ is correct?

$A \propto T^1$

$A \propto T^2$

$A \propto T^3$

$A \propto T^4$

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

Consider the motion of a particle along the $x$-axis. The position of the particle varies with time as $x(t)=\sin ^2(\omega t) \cos ^3(\omega t)$, where $\omega$ is a constant. What is the time period of the motion?

$\frac{2 \pi}{\omega}$

$\frac{2 \pi}{3 \omega}$

$\frac{2 \pi}{5 \omega}$

$\frac{2 \pi}{15 \omega}$

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

Consider a solid sphere of radius $R$ floating in a pond with half of the sphere submerged. The sphere is pushed vertically downwards at the topmost point and released, such that it executes a simple harmonic motion. Acceleration due to gravity is $g$. What is the time period of oscillation?

$2 \pi \sqrt{\frac{2 R}{g}}$

$2 \pi \sqrt{\frac{R}{g}}$

$2 \pi \sqrt{\frac{3 R}{2 g}}$

$2 \pi \sqrt{\frac{2 R}{3 g}}$

IAT (IISER) 2022

MCQ (Single Correct Answer)

-1

As shown in the figure a block is resting on a frictionless floor and is attached to the free end of a spring. The right edge of the block in equilibrium is at a distance $d$ from the wall. When the spring is compressed by a distance $d / 2$ and released, the time-period of the motion is $T$. Similarly, when compressed by a distance $2 d$ and released, the time-period is $T_0$. Considering elastic collision between the block and the wall, what is the value of the quantity $T_0 / T$ ? IAT (IISER) 2022 Physics - Simple Harmonic Motion Question 1 English

IAT (IISER) 2022 Physics - Simple Harmonic Motion Question 1 English

$1 / 4$

$3 / 4$

$2 / 3$

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