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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
0.3 kgk = 80 N/m

A 0.3 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.3 kgk = 80 N/m
f = Hz
2.Easy
3.8 kgk = ?

A 3.8 kg mass on a spring oscillates with a period of 2.4 s. Find the spring stiffness k.

m = 3.8 kgT = 2.4 s
k = N/m
3.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
4.Medium
L = 1.2 mT = 2.06 s

An astronaut on another planet finds that a simple pendulum 1.2 m long has a period of 2.06 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.2 mT = 2.06 s
g = m/s²
5.Hard
3.1 kgk = 170 N/mA = 8 cm

A 3.1 kg mass on a spring with k = 170 N/m is pulled 8 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.1 kgk = 170 N/mA = 8 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?12

A body oscillates in simple harmonic motion with period 2.1 s and amplitude 20 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 12 cm?

T = 2.1 sA = 20 cmx = 12 cm
t = s

Answer key

  1. 1. f = 2.599 Hz
  2. 2. k = 26.04 N/m
  3. 3. L = 1.553 m
  4. 4. g = 11.16 m/s²
  5. 5. vmax = 0.5924 m/s
  6. 6. t = 0.2151 s

Full step-by-step solutions: practise this topic on examproblems.com.