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
4.1 kgk = ?

A 4.1 kg mass on a spring oscillates with a period of 1.95 s. Find the spring stiffness k.

m = 4.1 kgT = 1.95 s
k = N/m
2.Easy
0.4 kgk = 40 N/m

A 0.4 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.4 kgk = 40 N/m
f = Hz
3.Medium
L = 2.3 m

A simple pendulum has a length of 2.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.3 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
5.Hard
mk = 280 N/mA = 4 cmx = 1 cm

A mass on a spring with k = 280 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its kinetic energy K when it is 1 cm from equilibrium.

k = 280 N/mA = 4 cmx = 1 cm
K = J
6.Hard
t (s)x (cm)t = ?8.4

A body oscillates in simple harmonic motion with period 0.9 s and amplitude 12 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 8.4 cm?

T = 0.9 sA = 12 cmx = 8.4 cm
t = s

Answer key

  1. 1. k = 42.57 N/m
  2. 2. f = 1.592 Hz
  3. 3. T = 3.042 s
  4. 4. L = 1.68 m
  5. 5. K = 0.21 J
  6. 6. t = 0.1111 s

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