Oscillations

As shown in the figures, a uniform rod $O O^{\prime}$ of length $l$ is hinged at the point $O$ and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected…

The center of a disk of radius $r$ and mass $m$ is attached to a spring of spring constant $k$, inside a ring of radius $R>r$ as shown in the figure. The other end of the spring is attached on the periphery of the ring.…

Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies $\omega_{1}$ and $\omega_{2}$ and have total energies $E_{1}$ and $E_{2}$ , respectively. The variations of…

A particle of mass $m$ is attached to one end of a massless spring of force constant $k$, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its…

A point mass is subjected to two simultaneous sinusoidal displacements in $x$-direction, $x_1(t)=A \sin \omega t$ and $x_2(t)=A \sin \left(\omega t+\frac{2 \pi}{3}\right)$. Adding a third sinusoidal displacement…

A wooden block performs SHM on a frictionless surface with frequency $v_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\mathbf{E}$ is switched on as shown, then the SHM of the block…

Paragraph: Phase space diagrams are useful tools in analyzing all kinds of dynamical problems. They are especially useful in studying the changes in motion as initial position and momentum are changed. Here we consider…

A metal rod of length $L$ and mass $m$ is pivoted at one end. A thin disc of mass $M$ and radius $R(< L)$ is attached at its centre to the free end of the rod. Consider two ways the disc is attached. Case A-the disc is…

Paragraph: When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$, it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be…

Paragraph: When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$, it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be…

Paragraph: When a particle of mass $m$ moves on the $x$-axis in a potential of the form $V(x)=k x^2$, it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt{\frac{m}{k}}$, as can be…

The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is