The amplitude of a wave represented by displacement equation
$y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be
Medium
Download our app for free and get started
Ideal equation
$y=\sqrt{\left(\frac{1}{\sqrt{a}}\right)^{2}+\left(\frac{1}{\sqrt{b}}\right) \sin (\omega t+\phi)}$
$\mathrm{y}=\left(\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}}\right) \sin (\omega \mathrm{t}+\phi)$
amplitude $A=\sqrt{\frac{1}{a}+\frac{1}{b}}=\sqrt{\frac{a+b}{a b}}$
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
- 1The equation of a simple harmonic motion is $X = 0.34\cos (3000t + 0.74)$ where $X$ and $t$ are in $mm$ and $sec$. The frequency of motion isView Solution
- 2$A$ particle of mass m is constrained to move on $x$ -axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example, when the particle is to the left of $E, F$ points to the right. The magnitude of $F$ is a constant $F$ except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards left from the equilibrium position $E$ and released from rest at $t = 0.$ Find minimum time it will take to reach from $x = - \frac{A}{2}$ to $0$.View Solution
- 3A simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string isView Solution
- 4View SolutionIf the metal bob of a simple pendulum is replaced by a wooden bob, then its time period will
- 5A pendulum clock that keeps correct time on the earth is taken to the moon it will run (it is given that $g_{Moon} = g_{Earth}/6$ )View Solution
- 6Two identical spring of constant $K$ are connected in series and parallel as shown in figure. A mass $m$ is suspended from them. The ratio of their frequencies of vertical oscillations will beView Solution
- 7Two simple harmonic motions are represented by the equations $x_{1}=5 \sin \left(2 \pi t+\frac{\pi}{4}\right), x_{2}=5 \sqrt{2}(\sin 2 \pi t+\cos 2 \pi t)$ The ratio of the amplitude of $x_{1}$ and $x_{2}$ isView Solution
- 8View SolutionFor a particle executing simple harmonic motion, which of the following statements is not correct
- 9A simple pendulum hanging from the ceiling of a stationary lift has a time period $T_1$. When the lift moves downward with constant velocity, the time period is $T_2$, thenView Solution
- 10The displacement of a particle is represented by the equation $y = sin^3\,\,\,\omega t$ . The motion isView Solution