b) Consider a particle undergoing simple harmonic motion. The velocity

Question

b) Consider a particle undergoing simple harmonic motion. The velocity of the particle at position $x_{1}$ is $v_{1}$ and velocity of the particle at position $x^{2}$ is $v_{2}.$ Show that the ratio of time period (T) and amplitude (A) is:

$\frac{T}{A}=2\pi\sqrt{\frac{x_2^{2}-x_{1}^{2}}{v_{2}^{1}x_{2}^{2}-v_{2}^{2}x_{1}^{2}}}$

10 Mar 2024

Answer :

Word Count : 350

To show the ratio of the time period (T) to the amplitude (A) for a particle undergoing simple harmonic motion (SHM) based on the given conditions, we can start with the equation for velocity in SHM. ### Step 1: Equation of motion for simple harmonic motion (SHM) In SHM, the total mechanical energy is conserved. The energy at any point is the sum of kinetic energy and potential energy, and ______ ___ ________ ________ _________ ___ ___ __________ _______ ____ ________.
_________ ________ _____ _____ _________ _______ ___ __________ _____ ______ _______.
_________ ___ _____ ____ ____ ______ ______.
______ _____ __________ _________ _________.
___ ___ ____ ________ ____ ________ ___.
________ _______ _________ ________ __________ ____ _________ _____ ______ ________ ___ _____.
_________ _______ __________ __________ ____ ____.
_______ ___ ______ ___ ________ __________ _________ _________ _____.
________ ____ ______ _______ ________ __________ ____ _______ _______.
__________ ________ ____ ____ ________ ______ _______ _________.
_________ __________ ___ _______ ____ ____ ____ _____ ______.
_____ ____ ______ _______ _____ ____.
______ ______ _______ _____ ______ _____.
________ ______ _______ ____ __________ ___ _____ __________ _____.
__________ _____ ____ _______ _________ _____ __________.
________ ______ ______ ____ _______ ________ ___ _____ _________.
____ ___ ___ ____ ___.
__________ _______ ___ ___ _______ __________ _______ ___ __________ _____ _______ __________.
______ ____ ______ _________ ___ _________.
______ ___ ______ ____ ________ ______ __________ ____ ___ ________ ______.
_______ _________ ____ __________ _______ ____ ______ ________.
____ ___ ________ __________ ______ ____.
____ _________ ____ _______ _____.
________ _______ ___ ______ __________ _____ __________ ________ ________.
____ ____ _________ _______ ___ ____ _______ ________.
__________ ___ _____ ______ _____ _______ _______ _________ ___ _________ ____ _____.
___ ______ _______ _________ __________.
___ _________ ___ ________ _______ _____ ______ _____ ________ _______ _________ ___.
___ _______ ___ _________ __________ _____ _________ ___ _________ ___ __________.
_________ ________ ___ __________ _____ ___ ____.
_________ _________ ________ __________ _____ ____.
__________ _________ ___ _________ ________ _________ __________ ________ _____ __________ _______.
_______ _________ ____ _________ ____ ___ __________ ______.
____ ______ _______ ____ ______ _________ __________.
Get Full Answer on WhatsApp

Related Questions

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers

IGNOU NEWS

Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★