For forced oscillations, the displacement is given by x=Asin(ωt+ϕ) with A=ω02−ω2F0/m
A particle of mass m is attached to a spring (of spring constant k ) and has a natural angular frequency ω0. An external force F(t) proportional to cosωt(ω=ω0) is applied to the oscillator. The time displacement of the oscillator will be proportional to
Held on 30 Apr 2004 · Verified 6 Jul 2026.
ω02−ω2m
m(ω02−ω2)1
m(ω02+ω2)1
ω02+ω2m
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The equation of a plane progressive wave is given by $y = 5\cos\pi\left(200t - \dfrac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is _______ m/s.
A transverse wave on a string is described by $y = 3\sin(36t + 0.018x + \pi/4)$, where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer) ($\pi = 3.14$)
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A spring-mass system oscillates with angular frequency ω. If the mass is doubled and the spring constant is halved, the new angular frequency is:
The time period of a simple harmonic oscillator is $T=2 \pi \sqrt{\frac{k}{m}}$. Measured value of mass $(m)$ of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant $(k)$ is $\_\_\_\_$ \%.
Work through every JEE Main Waves & Oscillations PYQ, year by year.