Question

A physics lab demonstrates the principles of simple harmonic motion (SHM) by using a spring affixed to a horizontal support. The student is asked to find the spring constant, k. After suspending a mass of 295.0 g from the spring, the student notices the spring is displaced by 49.5 cm from equilibrium. With this information, calculate the spring constant. = ___________ N/m The student realizes that the spring demonstrates SHM with the attached mass of 295.0 g. The student is next asked to calculate the period of oscillation, T, neglecting the mass of the spring. = ___________ s

For the final section of the lab, the student is asked to investigate the energy distribution of the spring system described above. Calculate the velocity and potential energy for each displacement given and insert the correct answer using the "choices" column.

Answer 1

F = ky

Mg = ky

K = Mg/y

K = 0.295 x 9.8 /0.495

= 5.84 N/m

T = 2π√(M/k)

= 2 x 3.14x √(0.295 / 5.84)

= 1.41 s

Velocity v = y x √(k/m) x √(a²-y²)

A = ky/m = 9.8

So v = 21.56 m/s

Potential energy PE = ½ ky²

= 5.84 * 0.495² / 2

= 0.715473 J