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
1.6 kgk = 220 N/m

A 1.6 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.6 kgk = 220 N/m
f = Hz
2.Easy
1.1 kgk = 310 N/m

A 1.1 kg mass on a spring with stiffness 310 N/m oscillates on a frictionless surface. Find the period T.

m = 1.1 kgk = 310 N/m
T = s
3.Medium
t (s)x (cm)1.4 s

A 3.7 kg mass on a spring with k = 320 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.4 s (with sign).

m = 3.7 kgk = 320 N/mA = 13 cmt = 1.4 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.5 s? Use g = 9.81 m/s². Find L.

T = 2.5 sg = 9.81 m/s²
L = m
5.Hard
1.9 kgk = 460 N/mA = 14 cm

A 1.9 kg mass on a spring with k = 460 N/m is pulled 14 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.9 kgk = 460 N/mA = 14 cm
E = J
6.Hard
t (s)x (cm)t = ?7.2

A body oscillates in simple harmonic motion with period 1.4 s and amplitude 12 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 7.2 cm?

T = 1.4 sA = 12 cmx = 7.2 cm
t = s

Answer key

  1. 1. f = 1.866 Hz
  2. 2. T = 0.3743 s
  3. 3. x = 11.69 cm
  4. 4. L = 1.553 m
  5. 5. E = 4.508 J
  6. 6. t = 0.1434 s

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