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
1.7 kgk = ?20 cm

Hanging a 1.7 kg mass on a spring stretches it by 20 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.7 kgx = 20 cmg = 9.81 m/s²
k = N/m
2.Easy
0.7 kgk = 350 N/m

A 0.7 kg mass on a spring with stiffness 350 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 350 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.2 s

A 2.3 kg mass on a spring with k = 340 N/m is pulled 11 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.2 s (with sign).

m = 2.3 kgk = 340 N/mA = 11 cmt = 0.2 s
v = m/s
5.Hard
3.5 kgk = 170 N/mA = 19 cm

A 3.5 kg mass on a spring with k = 170 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.5 kgk = 170 N/mA = 19 cm
amax = m/s²
6.Hard
2.3 kgk = 300 N/mA = 19 cm

A 2.3 kg mass on a spring with k = 300 N/m is pulled 19 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.3 kgk = 300 N/mA = 19 cm
amax = m/s²

Answer key

  1. 1. k = 83.38 N/m
  2. 2. T = 0.281 s
  3. 3. L = 0.3578 m
  4. 4. v = −0.8717 m/s
  5. 5. amax = 9.229 m/s²
  6. 6. amax = 24.78 m/s²

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