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
2.3 kgk = 30 N/m

A 2.3 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the period T.

m = 2.3 kgk = 30 N/m
T = s
2.Easy
2.7 kgk = ?8 cm

Hanging a 2.7 kg mass on a spring stretches it by 8 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.7 kgx = 8 cmg = 9.81 m/s²
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
4.Medium
L = 1.3 mT = 2.41 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 2.41 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 2.41 s
g = m/s²
5.Hard
2.3 kgk = 170 N/mA = 2 cm

A 2.3 kg mass on a spring with k = 170 N/m is pulled 2 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.3 kgk = 170 N/mA = 2 cm
amax = m/s²
6.Hard
t (s)x (cm)t = ?10.5

A body oscillates in simple harmonic motion with period 2.3 s and amplitude 14 cm. What is the shortest time t it needs to move from its maximum displacement of 14 cm to a displacement of 10.5 cm?

T = 2.3 sA = 14 cmx = 10.5 cm
t = s

Answer key

  1. 1. T = 1.74 s
  2. 2. k = 331.1 N/m
  3. 3. L = 2.236 m
  4. 4. g = 8.836 m/s²
  5. 5. amax = 1.478 m/s²
  6. 6. t = 0.2646 s

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