If we express position x(t)=Asin(ωt+ϕ) then x0=Asinϕv0=Aωcosϕ⇒tanϕ=v0ωx0A=x02+ω2v02 Hence both position and linear momentum of a particle can be expressed as a function of time if we know initial momentum and position
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Knowing initial position x0 and initial momentum p0 is enough to determine the position and momentum at any time t for a simple harmonic motion with a given angular frequency ω. Reason (R): The amplitude and phase can be expressed in terms of x0 and p0. In the light of the above statements, choose the correct answer from the options given below :
Held on 28 Jan 2025 · Verified 6 Jul 2026.
(A) is false but (R) is true
(A) is true but (R) is false
Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
Both (A) and (R) are true and (R) is the correct explanation of (A)
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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.