The displacement of a particle executing simple harmonic motion is given by
$\mathrm{y}=\mathrm{A}_{0}+\mathrm{A} \sin \omega \mathrm{t}+\mathrm{B} \cos \omega \mathrm{t}$
Then the amplitude of its oscillation is given by
NEET 2019, Medium
Download our app for free and get started
$y=A_{0}+A \sin \omega t+B \cos \omega t$
$y=A_{0}+\sqrt{A^{2}+B^{2}} \sin (\omega t+\phi)$
$\mathrm{A}_{0}$ is mean position, and $\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}$ is amplitude
Download our appand 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.*
Similar Questions
- 1A simple harmonic oscillator has an amplitude a and time period $T$. The time required by it to travel from $x = a$ to $x = \frac{a }{2}$ isView Solution
- 2A simple pendulum is suspended in a car. The car starts moving on a horizontal road according to equation $x\, = \,\frac{g}{2}\,\sqrt 3 {t^2}$. Find the time period of oscillation of the pendulum.View Solution
- 3The displacement $x$ (in metre) of a particle in, simple harmonic motion is related to time t (in seconds) asView Solution
$x = 0.01\cos \left( {\pi \,t + \frac{\pi }{4}} \right)$
The frequency of the motion will be
- 4silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12} /sec$. What is the force constant of the bonds connecting one atom with the other? ................ $\mathrm{N/m}$ (Mole wt. of silver $= 108 $ andAvagadro number $= 6.02 \times 10^{23}$ $gm \ mole^{ -1}$ )View Solution
- 5A rod of mass $m$ and length $l$ is suspended from ceiling with two string of length $l$ as shown. When the rod is given a small push in the plane of page and released time period is $T_1$ and when the rod is given a push perpendicular to plane time period of oscillation is $T_2$ . The ratio $\frac{{T_1^2}}{{T_2^2}}$ isView Solution
- 6If a simple harmonic oscillator has got a displacement of $0.02\, m$ and acceleration equal to $2.0\,m{s^{ - 2}}$ at any time, the angular frequency of the oscillator is equal to .... $rad\,{s^{ - 1}}$View Solution
- 7The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ isView Solution
- 8Two simple harmonic motions are represented by the equationsView Solution
${x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$ and ${x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})$
The amplitude of second motion is ....... times the amplitude in first motion.
- 9A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then, its time period of vibration will beView Solution
- 10An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross$-$section, $A$. Young modulus of the material of the wire is $Y$. If the mass is pulled down slightly its frequency of oscillation along the vertical direction isView Solution