Physics Oscillations

As we know that maximum acceleration will act on the particle when it is at extreme position .

$\omega =\frac{\frac{\pi }{6}}{0.1}=\frac{10\pi }{6}$

$f=m{\omega }^{2}x$

$\frac{f}{m}={\omega }^{2}A=\frac{1000{\pi }^2}{36}*0.36={\pi }^2=9.87N$

$T^{\prime }=2\pi \sqrt[]{\frac{{?}^{\prime }}{g}}$ where $t^{\prime }=\frac{\mathcal{l}}{2}$

$T=2\pi \sqrt[]{\frac{t}{g}}$

$T^{\prime }=\frac{x}{2}T$

$2\pi \sqrt[]{\frac{t}{2g}}=\frac{x}{2}2\pi \sqrt[]{\frac{t}{g}}$

$\frac{1}{\sqrt[]{2}}=\frac{x}{2}\Rightarrow x=\sqrt[]{2}$

$T=m\widehat{?}{\omega }^2$

$T^{\prime }=m:{(2\omega )}^2$

$T^{\prime }=4T$

$$For SHM, kinetic and potential energies are equal when displacement $x=\pm \frac{A}{\sqrt{2}}$ , where A is the amplitude. At this point, total energy is evenly shared between motion and position-dependent restoring forces.

In SHM, the restoring force, F is directly proportional to the negative of displacement. That is, F=- kx. This follows Hooke's law and ensures motion is oscillatory about the mean position with angular frequency,  

$\omega =\sqrt{\frac{k}{m}}$

Uniform circular motion has constant speed. But SHM requires velocity and acceleration to vary sinusoidally with displacement. SHM is the projection of uniform circular motion. But it's not the motion itself, due to differing energy and force characteristics.

x = A sin $\omega t$

$\Rightarrow v=A\omega cos\omega t$

$\Rightarrow v=\pm \omega \sqrt[]{A^2-x^2}$

$\frac{v^2}{{\omega }^2}+x^2=A^2$

Elliptical

No, only oscillations with a linear restoring force and sinusoidal motion are SHM. Non-linear oscillations, such as large pendulum swings, deviate from SHM.

Oscillations are larger, slower to-and-fro motions. Vibrations, on the other hand, are smaller, faster oscillations. Vibrations often occur in machines, strings, and structural components.

No, periodic motion isn't always oscillatory. It may not involve back-and-forth movement about an equilibrium point. Some known examples include circular motion in satellites or planets.