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masoomaNaqvi:
a oscillating block -spring system has a mechanical energy of 1.00 j ,an amplitude of 10.0 cm , and a maximum speed of 1.20m/s . find (a) the spring constant, (b) the mass of the block and (c) the frequency of oscillation.
(a) Emec = (1/2)kA2
, so k = 2Emec/A2 = 2 · (1 J)/(0.1 m)2 = 200 N/m.
(b) Use the fact that Kmax = Emec = (1/2)mv2
max:
(1/2)mv2
max = 1 J ⇒ m = 2 · (1 J)/(1.2 m/s)2 = 1.39 kg.
(c) We get ω from the velocity equation and information, then use that to get f = ω/2π:
vmax = Aω = 1.20 m/s ⇒ ω = (1.20 m/s)/(0.1 m) = 12.0 rad/s.
f = 12.0/6.28 = 1.91 Hz.
, so k = 2Emec/A2 = 2 · (1 J)/(0.1 m)2 = 200 N/m.
(b) Use the fact that Kmax = Emec = (1/2)mv2
max:
(1/2)mv2
max = 1 J ⇒ m = 2 · (1 J)/(1.2 m/s)2 = 1.39 kg.
(c) We get ω from the velocity equation and information, then use that to get f = ω/2π:
vmax = Aω = 1.20 m/s ⇒ ω = (1.20 m/s)/(0.1 m) = 12.0 rad/s.
f = 12.0/6.28 = 1.91 Hz.
thank you so much
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