Answer to Question #89508 in Physics for Reign
2019-05-09T23:41:32-04:00
1. A 200.0 g mass vibrates in Simple Harmonic Motion with a total energy of 24.7 J and a frequency of 5.0 Hz.
(a) Find the spring constant k
(b) Find the maximum displacement
(c) Find the position, velocity and acceleration as a function of time.
1
2019-05-13T10:29:50-0400
a)
2 π f = k m 2\pi f=\sqrt{\frac{k}{m}} 2 π f = m k
2 π ( 5 ) = k 0.2 2\pi (5)=\sqrt{\frac{k}{0.2}} 2 π ( 5 ) = 0.2 k
k = 197 N m k=197 \frac{N}{m} k = 197 m N b)
E = 0.5 k A 2 E=0.5kA^2 E = 0.5 k A 2
A = 2 E k = 2 ( 24.7 ) 197 = 0.500 m A=\sqrt{\frac{2E}{k}}=\sqrt{\frac{2(24.7)}{197}}=0.500\ m A = k 2 E = 197 2 ( 24.7 ) = 0.500 m c)
x = A sin ( 2 π f t ) = 0.5 sin ( 10 π t ) x=A\sin{(2\pi ft)}=0.5\sin{(10\pi t)} x = A sin ( 2 π f t ) = 0.5 sin ( 10 π t )
v = 0.5 ( 10 π ) sin ( 10 π t ) = 5 π sin ( 10 π t ) v=0.5(10\pi)\sin{(10\pi t)}=5\pi \sin{(10\pi t)} v = 0.5 ( 10 π ) sin ( 10 π t ) = 5 π sin ( 10 π t )
a = − 0.5 ( 10 π ) 2 sin ( 10 π t ) = − 50 π 2 sin ( 10 π t ) a=-0.5(10\pi)^2\sin{(10\pi t)}=-50\pi^2\sin{(10\pi t)} a = − 0.5 ( 10 π ) 2 sin ( 10 π t ) = − 50 π 2 sin ( 10 π t )
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