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A particle is moving with shm in a strai...

A particle is moving with shm in a straight line. When the distance of the particle from the equilibrium position has the value `x_1 and x_2` the corresponding values of velocities are `v_1 and v_2` show that period is `T=2pi[(x_2^2-x_1^2)/(v_1^2-v_2^2)]^(1//2)`

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To solve the problem, we need to use the principles of simple harmonic motion (SHM) and the conservation of energy. Let's break it down step by step. ### Step 1: Understand the Energy Conservation in SHM In SHM, the total mechanical energy (E) of the system is conserved and is the sum of kinetic energy (KE) and potential energy (PE). The total energy at any position can be expressed as: \[ E = KE + PE \] ### Step 2: Write the Energy Expressions at Positions \(x_1\) and \(x_2\) At position \(x_1\): ...
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