Answer to Question #89508 in Physics for Reign

Question #89508
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
Expert's answer
2019-05-13T10:29:50-0400

a)


2πf=km2\pi f=\sqrt{\frac{k}{m}}

2π(5)=k0.22\pi (5)=\sqrt{\frac{k}{0.2}}

k=197Nmk=197 \frac{N}{m}

b)


E=0.5kA2E=0.5kA^2

A=2Ek=2(24.7)197=0.500 mA=\sqrt{\frac{2E}{k}}=\sqrt{\frac{2(24.7)}{197}}=0.500\ m

c)


x=Asin(2πft)=0.5sin(10πt)x=A\sin{(2\pi ft)}=0.5\sin{(10\pi t)}

v=0.5(10π)sin(10πt)=5πsin(10πt)v=0.5(10\pi)\sin{(10\pi t)}=5\pi \sin{(10\pi t)}

a=0.5(10π)2sin(10πt)=50π2sin(10πt)a=-0.5(10\pi)^2\sin{(10\pi t)}=-50\pi^2\sin{(10\pi t)}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment