A 5.0-kg block, initially at rest on a level, frictionless surface, is attached

Question

A 5.0-kg block, initially at rest on a level, frictionless surface, is attached to a Hooke's Law spring with spring constant k= 80 N/m. The spring, which is also level, is rigidly attached to a wall on the other end as shown in the diagram above. Also assume that there is no friction in the spring or at the point of attachment. The block is then streched from its equilibrium position at x= 0.00 m to a distance of 50 cm to the right and released. Taking the initial time to be t = 0.00s at the release point, answer the following:

Find the position, velocity, and acceleration of the mass at t= 1.2 s. (Since position, velocity, and acceleration are all vectors, the signs of the answers are also important)

Explanation / Answer

Spring will oscillate with a time period

=2m/k=3.3 seconds

x(t)=.5cost because t=0 x=.5 m

dx/dt=-.5sint      d2 x/dt2 =-.52 cost

=k/m=4    at t=1.2 sec

x=.5cos4.8 = 4 cm v=.5x4xsin 4.8 =1.98 m/sec (in the direction to wards spring initial position)

a=8cos4.8 (decreasing velocity) =.66 m/s2

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