Q1) A left traveling wave with a maximum amplitude of 6cm has frequency of 95.49

Question

Q1) A left traveling wave with a maximum amplitude of 6cm has frequency of 95.49hz. How long does it take for the wave between -2cm and 2 cm ? (Hint:  first write down a function which you think describes this wave )  

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Q2) A 6 kg mass oscillates on a spring according to the following measurments Vmax= 10 m/s , Amplitude= 0.7m , and period of 3 seconds . A)What is the angular velocity (w) ? B)What is the spring constant used for the oscillation ? C)Draw the velocity vs. time and acceleration vs. time graphs of this oscillation given the position vs. time graph , be sure to lable axis with important points ?

A left traveling wave with a maximum amplitude of 6cm has frequency of 95.49hz. How long does it take for the wave between -2cm and 2 cm ? (Hint: first write down a function which you think describes this wave )

Explanation / Answer

Q.1)

this wave is represent by eqution:

x(t) = A*cos(wt)

==>

so,

2 = 6*cos(95.49*t1) ..(1)

arccos(2/6) = (95.49*t1)

==> 70.5287794 degree =  (95.49*t1)

==> t1 = 70.5287794/95.49 = 0.7386 sec

-2 = 6*cos(95.49*t2)...(2)

so,

t2 = arccos(-2/6)/95.49 = 109.471221/95.49 = 1.146 sec

so,

t2-t1 = 1.146-0.7386 = 0.4074 sec

Q.2)

A) k = 4*pi^2*m/T^2 = 4*pi^2*6/3^2 = 26.32 N/m

w = sqrt(k/m) = sqrt(26.32/6) = 2.09 rad/sec

B) k =  4*pi^2*m/T^2 = 4*pi^2*6/3^2 = 26.32 N/m

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