mass is vibrating at the end of a spring with a spring constant 1.37 N/m. The fi

Question

mass is vibrating at the end of a spring with a spring constant 1.37 N/m. The figure shows a graph of its position x (in centimetres) as a function of time t (in seconds). At what time between t=0 s and the first maximum after t=0 s is the mass not moving?

graph: http://capa.phys.dal.ca/dalphysicslib/Graphics/Gtype27/prob01.4.gif

A)What is the magnitude of the acceleration of the object at the second maximum in the x-t curve after t = 0 s?

B)What is the mass of the object?

Correct, computer gets: 8.88e-02 kg

C)How much energy did the system originally contain?

Correct, computer gets: 2.47e-03 J

D)How much energy did the system lose between t = 0 s and the third maximum after t = 0 s? Think about where this energy has gone.

Explanation / Answer

if the particle vibrating simple harmonically from the mean position ,the velocity is maximum at the mean position and zero at the extreme position. so from the graph at t = 0.8 s between t=0 s and the first maximum after t=0 s the mass not moving.

(A)

Acceleration = A*(2*pi*f)2

from the graph A = 2.4cm , T = 1.6 , f = 1/1.6 = 0.625

Acceleration = 0.024*(2*3.14*0.625)2  = 0.369 m/s2

(B)

T = 2*pi*sqrt(m/k)

1.6 = 2*3.14*sqrt(m/1.37)

m = 8.88*10-2 kg

(C)

the system is at the extreme position at x = 6 cm = 0.06m

E=(1/2)kx^2 = 0.5*1.37*(0.06)2

E= 0.00246 J =2.46 mJ

(d)

Energy at third maxima after t=0 ,

E'=0.5*1.37*(0.018)2= 0.000221J = 0.221 mJ

So energy lose = 2.46 - 0.221 =2.239 mJ

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