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
3.4 kgk = 50 N/m

A 3.4 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 3.4 kgk = 50 N/m
T = s
2.Easy
2.4 kgk = ?

A 2.4 kg mass on a spring oscillates with a period of 2.4 s. Find the spring stiffness k.

m = 2.4 kgT = 2.4 s
k = N/m
3.Medium
0.7 kgk = 280 N/mA = 20 cmx = 15 cm

A 0.7 kg mass on a spring with k = 280 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its speed v when it is 15 cm from equilibrium.

m = 0.7 kgk = 280 N/mA = 20 cmx = 15 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1 s? Use g = 9.81 m/s². Find L.

T = 1 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?9

A body oscillates in simple harmonic motion with period 0.8 s and amplitude 15 cm. What is the shortest time t it needs to move from its maximum displacement of 15 cm to a displacement of 9 cm?

T = 0.8 sA = 15 cmx = 9 cm
t = s
6.Hard
2 kgk = 1000 N/m500 m/s

A 12 g bullet moving at 500 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1000 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 500 m/sM = 2 kgk = 1000 N/m
A = cm

Answer key

  1. 1. T = 1.638 s
  2. 2. k = 16.45 N/m
  3. 3. v = 2.646 m/s
  4. 4. L = 0.2485 m
  5. 5. t = 0.1181 s
  6. 6. A = 13.38 cm

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