Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
0.9 kgk = 400 N/m

A 0.9 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the period T.

m = 0.9 kgk = 400 N/m
T = s
2.Easy
4.9 kgk = ?

A 4.9 kg mass on a spring oscillates with a period of 2.45 s. Find the spring stiffness k.

m = 4.9 kgT = 2.45 s
k = N/m
3.Medium
t (s)x (cm)0.9 s

A 3.4 kg mass on a spring with k = 310 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.9 s (with sign).

m = 3.4 kgk = 310 N/mA = 10 cmt = 0.9 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
3.5 kgk = 1400 N/m450 m/s

An 8 g bullet moving at 450 m/s hits and stays in a 3.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1400 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 8 gv = 450 m/sM = 3.5 kgk = 1400 N/m
A = cm
6.Hard
0.5 kgk = 1500 N/m200 m/s

A 20 g bullet moving at 200 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1500 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 200 m/sM = 0.5 kgk = 1500 N/m
A = cm

Answer key

  1. 1. T = 0.298 s
  2. 2. k = 32.23 N/m
  3. 3. x = −6.741 cm
  4. 4. L = 0.8051 m
  5. 5. A = 5.137 cm
  6. 6. A = 14.32 cm

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