Embibe Experts Solutions for Chapter: Simple Harmonic Motion, Exercise 2: Exercise - 2

A particle performs simple harmonic motion at a frequency $f$. The frequency at which its kinetic energy varies is:

A horizontal plank has a rectangular block placed on it. The plank starts oscillating vertically and simple harmonically with an amplitude of $40 \mathrm{cm}$. The block just loses contact with the plank when the latter is at momentary rest. Then:

As shown in the figure a horizontal platform with a mass $m$ placed on it is executing SHM along $y$-axis. If the amplitude of oscillation is $2.5 \mathrm{cm}$, the minimum period of the motion for the mass not to be detached from the platform is: $(g= 10 \mathrm{m} {\sec }^{-2} = {\mathrm{\pi }}^2)$ 

For a body executing SHM with amplitude $A$, time period $T$, maximum velocity $v_{\max }$ and phase constant zero, which of the following statements are correct for $0\le t\le \frac{T}{4}$ ($y$ is displacement from mean position)?

A ball is hung vertically by a thread of length '' from a point$\text{'}\mathrm{P}\text{'}$of an inclined wall that makes an angle $\text{'}\mathrm{\alpha }\text{'}$with the vertical. The thread with the ball is then deviated through a small angle $\text{'}\mathrm{\beta }\text{'} (\mathrm{\beta }>\mathrm{\alpha })$ and set free. Assuming the wall to be perfectly elastic, the period of such pendulum is/are 

If SHM is given by, $y=(\mathrm{sin\omega }t+\mathrm{cos\omega }t)m$, which of the following statements are true?

The position of a particle at time $t$ moving in $\mathrm{x}-\mathrm{y}$ plane is given by $\overrightarrow{r}=(\hat{\mathrm{i}}+ 2\hat{\mathrm{j}})A\mathrm{cos\omega t}$ Then, the motion of the particle is : 

Three simple harmonic motions in the same direction having the same amplitude $a$ and same time periods are superimposed. If each differs in phase from the next by $45°$, then: