KEAM 2018

A wave along a string has the following equation $y=0.05\sin (28t-1.78x) \mathrm{m}$ (where, $t$ is in seconds and $x$ is in meters). What are the amplitude $\left(A\right),$ frequency $\left(f\right)$ and wavelength $\left(\lambda \right)$ of the wave ?

A particle of mass $m$ is moving along the $x-\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{s}$ under the potential  $V(x)=\frac{k{x}^2}{2}+\frac{\lambda }{x^{\prime }}$  where $k$ and  $x^{\prime }$ are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency $\left(\omega \right)$ given by

A body undergoing simple harmonic motion has a maximum acceleration of $8 \mathrm{m} {\mathrm{s}}^{-2}$ and maximum speed of $1.6 \mathrm{m} {\mathrm{s}}^{-1}.$ What is the time period $T ?$

Instantaneous power delivered to a damped harmonic oscillator (natural frequency is ${\omega }_0),$ by an external periodic force (driving frequency $\omega )$ under steady state conditions is

The velocity and acceleration of a particle performing simple harmonic motion have a steady phase relationship. The acceleration shows a phase lead over the velocity in radians of

Two simple harmonic motions with the same amplitude and same frequency acting in the same direction are impressed on a particle. If the resultant amplitude of the particle is equal to the amplitude of individual $\mathrm{S}.\mathrm{H}.\mathrm{M}.\mathrm{s}$, the phase difference between the two simple harmonic motions is