If $x = a\sin \left( {\omega t + \frac{\pi }{6}} \right)$ and $x' = a\cos \omega t$, then what is the phase difference between the two waves
A$ \pi/ 3$
B$ \pi/ 6$
C$ \pi/ 2$
D$ \pi$
Medium
Download our app for free and get started
A$ \pi/ 3$
a (a) $x = a\sin \left( {\omega t + \frac{\pi }{6}} \right)$ and $x' = a\cos \omega t = a\sin \,\left( {\omega \,t + \frac{\pi }{2}} \right)$
$\therefore \Delta \phi = \left( {\omega t + \frac{\pi }{2}} \right) - \left( {\omega t + \frac{\pi }{6}} \right) = \frac{\pi }{3}$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
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 $(4/3) ×1000 kg/m^3$. What relationship between $t$ and ${t_0}$ is true
A body oscillates with a simple harmonic motion having amplitude $0.05\, m .$ At a certain instant, its displacement is $0.01\, m$ and acceleration is $1.0 \,m / s ^{2} .$ The period of oscillation is
Two damped spring-mass oscillating systems have identical spring constants and decay times. However, system $A's$ mass $m_A$ is twice system $B's$ mass $m_B$ . How do their damping constants, $b$ , compare ?
A particle starts from a point $P$ at a distance of $A/2$ from the mean position $O$ and travels towards left as shown in the figure. If the time period of $SHM$ , executed about $O$ is $T$ and amplitude $A$ then the equation of motion of particle is
Two simple harmonic motions are represented by equations ${y_1} = 4\,\sin \,\left( {10t + \phi } \right)$ and ${y_2} = 5\,\cos \,10\,t$ What is the phase difference between their velocities?
A pendulume clock loses $12\;s$ a day if the temperature is $40^oC$ and gains $4\;s$ a day if the temperature is $20^oC$. The temperature at which the clock will show correct time, and the coeffecient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively