Write your work out as though you are explaining things to someone who has not s

Question

Write your work out as though you are explaining things to someone who has not seen or thought about the problem before. When sketching a graph, you do not need to make the axes at a precise scale or provide precise numerical values. However, you must accurately label the axes. If you are drawing some other type of diagram, make sure to label all important elements clearly. When solving a problem quantitatively, show all essential steps (simple algebra or arithmetic can be skipped in your final write up). Describe your steps and your plan either in the of your solution or beforehand. Make sure a person who knows nothing about the problem understand your logic. If you quote a relationship or equation that is sot one of the principles, you should either Prove the relationship or equation using core principles OR Justify the relationship by briefly explaining in what physical circumstances. You are entitled to 1 page of double-sided notes.

Explanation / Answer

Given that x(t)= 0.05*cos(10^6*t)

a) period is T = 2*pi/w

comparing the given equation with the standard equation

x(t) = A*cos(w*t)

w is the angular speed

w = 10^6

then T = 2*pi/w = (2*3.142)/10^6 = 6.284*10^-6 sec

b) particle's velocity is v(t) = dx(t)/dt = -A*w*sin(w*t) = -0.05*10^6*sin(10^6*t)

c) particle's accelaration is a(t) = dv(t)/dt = -Aw^2*cos(w*t) = -0.05*(10^6)^2*cos(w*t)

d) at the equilibrium ,or at x = 0 ,the particle has maximum speed

vmax = A*w = 0.05*10^6 = 5*10^4 m/sec

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