The position of the center of the box shown is given by the equation: x = (4.7 m

Question

The position of the center of the box shown is given by the equation: x = (4.7 m) * cos(20(s-1) * t)

1)

What is the position of the box 4 seconds after the oscillations have started?

x =

m  

2)

What is the amplitude of the box's oscillations?

A =

m  

3)

What is the period of the box's oscillations?

T =

seconds  

4)

What is the box's maximum velocity?

vmax =

m/s  

5)

What is the box's maximum acceleration?

amax =

m/s2

6)

How long does it take the box to move from -2.35 m to +2.35 m?

t =

seconds  

Explanation / Answer

Solution: Oscillation of the position of the box is given by the eqn, x = 4.7 cos 20t.

(1) Putting t=4 sec, x = 0.816 m = position of the box 4 seconds after the oscillations have started.

(2) Comparing the given eqn with x = A cos ?t, we can infer that A = 4.7 m = the amplitude of the box's oscillations.

(3) Evidently, ? = 2?/T = 20. So, T = 0.314 sec = the period of the box's oscillations.

(4) vmax =

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