Download A block whose mass is 680 g is fastened to a spring whose spring

A block whose mass is 680 g is fastened to a spring whose spring constant k is 65 N/m. The
block is pulled a distance x = 11 cm from its equilibrium position at x = 0 and released from rest
at t = 0.
1. What are the angular frequency, the frequency, and the period of the resulting motion?
2. What is the amplitude of the oscillation?
3. What is the maximum speed of the oscillating block, and where is the block when it
occurs?
4. What is the magnitude of the maximum acceleration of the block?
5. What is the phase constant of the motion?
6. What is the total mechanical energy of the spring-block system?
7. What is the displacement function x(t) for the spring-block system?
1
A 3.00 kg mass is attached to a spring on a smooth horizontal surface. A horizontal force of 27N
is needed to hold the mass at rest when it is pulled 15 cm from its equilibrium position. The
mass is now released from rest with an initial displacement of 15 cm and it undergoes simple
harmonic oscillations.
1. Find the force constant of the spring
2. Find the frequency of the oscillations
3. Find the maximum speed. And where does this occur?
4. Find the maximum acceleration. And where does this occur?
5. Find the total energy of the system
6. Find the speed and acceleration when the displacement is one fifth of its maximum value.
2
A frictionless mass-spring system oscillates with an amplitude of 3.5 cm. If the spring constant
is 250 N/m and the mass is 0.500 kg, determine:
1. the total mechanical energy of the system
2. the maximum speed of the mass
3.
the maximum acceleration
3
The oscillations of a 0.25 kg mass on a spring with k = 85 N/m are damped (the damping force is
proportional to the velocity). If the oscillations amplitude is reduced by one-half in 5.0 s, find
the damping constant, b.
4