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State the expression for the total energy of a particle performing linear SHM. What conclusions can be drawn from the expression for the total energy ? |
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Answer» Solution :CONSIDER a particle of mass m performing SHM with AMPLITUDE A and period `T=(2pi)/(omega)'" where "omega=sqrt((k)/(m))` is the APPROPRIATE constant related to the system. The total energy of the particle is `E=(1)/(2) kA^(2)=(1)/(2) m omega^(2)A^(2)` Conclusions : The total energy of the particle (1) is independent of the position of the particle and thus remains constant when m, `omega and A` are constant, (2) is proportional to the mass of the particle `(E prop m),` (3) is proportional to the square of the amlitude `(E prop A^(2))`, (4) is inversely proportional to the square of the period T of the SHM (as `omega=2pi//T)`, (5) is proportional to the square of the frequency f of the SHM (as `omega=2pif`). |
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