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 kgk = 360 N/m

A 3 kg mass on a spring with stiffness 360 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3 kgk = 360 N/m
f = Hz
2.Easy
1 kgk = ?

A 1 kg mass on a spring oscillates with a period of 1 s. Find the spring stiffness k.

m = 1 kgT = 1 s
k = N/m
3.Medium
1.6 kgk = 440 N/mA = 12 cmx = 7 cm

A 1.6 kg mass on a spring with k = 440 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 7 cm from equilibrium.

m = 1.6 kgk = 440 N/mA = 12 cmx = 7 cm
v = m/s
4.Medium
t (s)x (cm)0.6 s

A 0.9 kg mass on a spring with k = 210 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.6 s (with sign).

m = 0.9 kgk = 210 N/mA = 4 cmt = 0.6 s
x = cm
5.Hard
mk = 50 N/mA = 7 cmx = 2 cm

A mass on a spring with k = 50 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find the energy U stored in the spring when the mass is 2 cm from equilibrium.

k = 50 N/mA = 7 cmx = 2 cm
U = J
6.Hard
t (s)x (cm)t = ?14

A body oscillates in simple harmonic motion with period 2.3 s and amplitude 20 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 14 cm?

T = 2.3 sA = 20 cmx = 14 cm
t = s

Answer key

  1. 1. f = 1.743 Hz
  2. 2. k = 39.48 N/m
  3. 3. v = 1.616 m/s
  4. 4. x = −3.866 cm
  5. 5. U = 0.01 J
  6. 6. t = 0.2838 s

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