A block with mass m = 5.3 kg is attached to two springs with spring constants k

Question

A block with mass m = 5.3 kg is attached to two springs with spring constants kleft = 33 N/m and kright = 48 N/m. The block is pulled a distance x = 0.26 m to the left of its equilibrium position and released from rest

1)Where is the block located, relative to equilibrium, at a time 1.09 s after it is released? (if the block is left of equilibrium give the answer as a negative value; if the block is right of equilibrium give the answer as a positive value)

2)What is the net force on the block at this time 1.09 s? (a negative force is to the left; a positive force is to the right)

3)What is the total energy stored in the system?

4)If the block had been given an initial push, how would the period of oscillation change?

Explanation / Answer

Solution:From the question the springs are in parallel, though seems to be in series.
The extreme ends are fixed and the block is connected to the other ends of each spring
---------------------------------------...
1)v² = (k1+ k2)*x²/m
v² = (33+ 48)*0.26²/5.3
v = 2.61m/s toward right.

2) = (k1+ K2)/m = [(33+ 48)*/5.3] = 3.90rad/s
x = A sin (t –/2) = 0.26 sin (3.90t - /2) (angles are in radians)
At time t = 1.09s
x = 0.0121m to the right of the equilibrium position,

F = -kx = - (33+48)*(0.0121) = - 0.9801 toward left

3)Total energy =0.5*(33+ 48)*0.2² = 1.62 J

4) Give the value of initial push

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.