2. calculate amplitude, A 3.calculate the constant, k 4. based on your results a

Question

2. calculate amplitude, A

3.calculate the constant, k

4. based on your results above write the equation for the position as a function of time x(t)=

5. calculate acceleration at t=0

6. calculate the speed at t=0

start out with x=Acos(wt + Phi), the position of a mass attached to an ideal spring placed ona frictionless spring, the mass is 1 kg the spring is constant and the maximum speed is 20 m/s and the angular frequencey is 20 rad/s. at t=0 the position is0.5 m from the equilibrium. find the following.... 1. calculate the phase angle, Phi 2. calculate amplitude, A 3.calculate the constant, k 4. based on your results above write the equation for the position as a function of time x(t)= 5. calculate acceleration at t=0 6. calculate the speed at t=0

Explanation / Answer

1. calculate the phase angle, Phi

It is 0.25 rad=14.32 deg
2. calculate amplitude, A

V=20 m/s=Aw

A=20/20=1 ,/s
3.calculate the constant, k

k=mw^2=1*20^2=400 kg/s^2
4. based on your results above write the equation for the position as a function of time x(t)=20sin(20t+phi)=5

20t+phi=0.25

at t=0,

phi=0.25

20sin(20t+0.25)
5. calculate acceleration at t=0

Alpha=-wx^2=0
6. calculate the speed at t=0

Speed=WA=20 m/s

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