Questions
The mean kinetic energy of a particle executing SHM over one full oscillation, given mass of particle = m, amplitude = A, angular frequency = ).
a
14mω2A2
b
12mω2A2
c
122mω2A2
d
18mω2A2
detailed solution
Correct option is A
x=Asinωt So,v=AωcosωtKE=12mv2=12m(Aωcosωt)2=12mω2A2cos2ωtMean kinetic energy = KEmean =∫0T (KE)dt∫∫T dt=∫0T 12mω2A2cos2ωtdtT=12mω2A2TT∫0T cos2ωtdt=12mω2A2(T)∫0T 1+cos2ωt2dt=12mω2A2Tt2+sin2ωt4ω0T=12mω2A2TT2=14mω2A2.Talk to our academic expert!
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