The angular velocity of the spring be $\omega$ $x=a \cos (\omega t+\theta)$ At $t=0, x=x_{0}$ On Substituting these values in the above equation we get, $\mathrm{x}_{0}=\mathrm{A} \cos \theta-(1)$...

Amplitude is given as $=5 \mathrm{~cm}=0.05 \mathrm{~m}$ Time period is given as $=0.2 \mathrm{~s}$ When the displacement is $y$, then acceleration is given as $A=-\omega^{2} y$ Velocity is given as...

Amplitude is given as $=5 \mathrm{~cm}=0.05 \mathrm{~m}$ Time period is given as $=0.2 \mathrm{~s}$ When the displacement is $y$, then acceleration is given as $A=-\omega^{2} y$ Velocity is given as...

Mass of the circular disc is given as $10 \mathrm{~kg}$ Period of torsional oscillation is given as $1.5 \mathrm{~s}$ Radius of the disc is given as $15 \mathrm{~cm}=0.15 \mathrm{~m}$ Restoring...

Area of cross-section of the U-tube is given as $A$ Density of the mercury column is given as $\rho$ Acceleration due to gravity is given as $g$ Restoring force, F = Weight of the mercury column of...

The centripetal acceleration supplied by the circular motion of the car, as well as the acceleration due to gravity, will be felt by the bob of the basic pendulum. Acceleration due to gravity is...

(a) The spring constant $k$ is proportional to the mass in the case of a simple pendulum. The numerator ($m$) and denominator ($d$) will cancel each other out. As a result, the simple pendulum's...

Acceleration due to gravity on the surface of moon is given as $g^{\prime}=1.7 \mathrm{~m} \mathrm{~s}^{-2}$ Acceleration due to gravity on the surface of earth is given as $g=9.8 \mathrm{~m}...

Angular frequency of the piston is given as $\omega=200 \mathrm{rad} / \mathrm{min}$ Stroke is given as$=1.0 \mathrm{~m}$ Amplitude is given as $A=1.0 / 2$ $=0.5 \mathrm{~m}$ The maximum speed...

(a) What is the maximum extension of the spring in the two cases? (b) If the mass in Fig. (a) and the two masses in Fig. (b) is released, what is the period of oscillation in each case? Solution:...

(a)$x=3 \sin (2 m t+\pi / 4)$ $=-3 \cos (2 \pi t+\pi / 4+\pi / 2)$ $=-3 \cos (2 \pi t+3 \pi / 4)$ $=-3 \cos (2 \pi t+3 \pi / 4)$ On comparing with the standard equation $A \cos (\omega t+\Phi)$, we...

Obtain the corresponding simple harmonic motions of the $x$-projection of the radius vector of the revolving particle $P$, in each case. Solution: (a) Time period is given as $t=2 \mathrm{~s}$...

Solution: Distance travelled by the mass sideways is given as $a=2.0 \mathrm{~cm}$ Angular frequency of oscillation can be calculated as, $\omega=\sqrt{k} / \mathrm{m}$ $=\sqrt{1200 / 3}$...

Determine<br>(i) the frequency of oscillations, (ii) maximum acceleration of the mass Solution: Spring constant is given as $\mathrm{k}=1200 \mathrm{~N} \mathrm{~m}^{-1}$ Mass is given as...

At positlon, t = 0, The given function is $x(t)=A \cos (\omega t+\phi).....(1)$ $\begin{array}{l} 1=A \cos (\omega \times 0+\phi)=A \cos \phi \\ A \cos \phi=1 \end{array}$ Differentiating equation...

Condition of SHM is stated below, Acceleration is directly proportional to negative of displacement of particle. If ' $\mathrm{a}$ ' is the acceleration, $\mathrm{x}$ is the displacement Then, for...

(a) Negative, Zero, Zero A basic harmonic motion is being performed by the particle. The particle's mean location is denoted by $O$. Its highest velocity is at the mean position $O$. Because the...

(a) Zero, Positive, Positive Points A and B are the path's two ends, with A-B=10cm and'O' being the path's halfway. Between the end locations, a particle moves in a linear simple harmonic motion....

(a) $3 \cos [4 \pi-2 \omega t]=3 \cos [2 \omega t-\pi / 4]$ The equation can be written in the form $\cos (\omega t+\phi)$. It is S.H.M with the period $2 \pi / 2 \omega=\pi / \omega$ (b) $\cos...

(a) $\sin \omega t-\cos \omega t$ =2[(1/2)sinωt-(1/2)cosωt] =\sqrt{2}[(1 / \sqrt{2}) \sin \omega t-(1 / \sqrt{2}) \cos \omega t] $=\sqrt{2}[\sin \omega t \times \cos (\pi / 4)-\cos...

(a) Because the motion is repeated in only one position, the depicted graph does not illustrate periodic motion. The full motion during one period must be repeated successively for a periodic...

(a) Motion is not periodic since it does not repeat itself after a set length of time. (b) The following graph depicts a periodic motion that repeats every 2 seconds.

(a) Simple harmonic motion (b) SHM is not periodic, although general vibrations of a polyatomic molecule about its equilibrium position are. The inherent frequencies of a polyatomic molecule are...

(a) The rotation of a hydrogen molecule around its mass centre is periodic. This is due to the fact that when a hydrogen molecule spins about its centre of mass, it returns to the same location...