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A particle on a spring executes simple harmonic motion. Ifthe total energy of the particle is doubled then(a)the period of oscillation will increase by a factor of

A particle on a spring executes simple harmonic motion. Ifthe total energy of the particle is doubled then(a)the period of oscillation will increase by a factor of

Grade:12th pass

2 Answers

Arun
25763 Points
one year ago
The time period (T) of vibrations varies inversely as the square root of the force constant (k) of the spring.2) The time period (T) of vibrations varies directly as the square root of the mass (m) of body attached to the string.So the time period of an object of mass m on a spring executes a simple harmonic motion is given by,So, T = 2π √m/kThus in simple harmonic motion, time period of the oscillation is independent of the amplitude.If the mass m of the particle is doubled, then the time period (T ') of the simple harmonic motion would be,T ' = 2π √2m/kSo, T '/ T = (2π √2m/k)/( 2π √m/k)= √2T ' = √2TFrom the above observation we conclude that, the period of oscillation will change by a factor of √2

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