JEE Main 2004 — Waves & Oscillations

A particle at the end of a spring executes simple harmonic motion with a period $t_1$, while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $\mathrm{t}$, then

A particle of mass $m$ is attached to a spring (of spring constant $k$ ) and has a natural angular frequency $\omega_0$. An external force $F(t)$ proportional to $\cos \omega t\left(\omega \neq \omega_0\right)$ is applied to the oscillator. The time displacement of the oscillator will be proportional to

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is $t_0$ in air. Neglecting frictional force of water and given that the density of the bob is $\left(\frac{4}{3}\right) \times 1000 \mathrm{~kg} / \mathrm{m}^3$. What relationship between $t$ and $t_0$ is true?

The total energy of particle, executing simple harmonic motion is

The displacement y of a particle in a medium can be expressed as $y=10^{-6} \sin (110 t+20 x+\pi / 4) m$, where $t$ is in seconds and $x$ in meter. The speed of the wave is

In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_1$ of the force, while the energy is maximum for a frequency $\omega_2$ of the force, then