Question

verticalspring A block with mass m =6.7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.27 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.5 m/s. The block oscillates on the spring without friction.

At t = 0.46 s what is the magnitude of the net force on the block?

Answer 1

The spring constant is

The angular frequency is calculated by

The total energy of the system is

So, the amplitude of the oscillations can be calculated using

The equation of the motion is given by

At time 0.46

At this position total spring force is

So, the total force acting on the block is

So, the net force acting on the block at t = 0.46 s is 56.88 N.