Springs in motion: period, frequency and graphs

Answer Key - Grade 11 Science Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   A mass on a spring has amplitude 0.05 m and period 0.5 s. What is its greatest speed, to 0.01 m/s, Esme?

   0.63 m/s
2. 2.

   A mass on a spring has amplitude 0.1 m and period 2 s. What is its greatest speed, to 0.01 m/s, Jun?

   0.31 m/s
3. 3.

   A student says a smaller pull makes each cycle quicker. Which reply fits OpenStax, Milo?

   • Yes; a shorter path takes less time
   • Yes; half the pull gives half the period
   • No; the period stays the same for a smaller pull
4. 4.

   A student says doubling the mass doubles the period. Which reply fits T = 2π√(m ÷ k), Noah?

   • No; the period grows by √2, about 1.41 times
   • No; a bigger swing is what changes the period
   • Yes; the period is proportional to the mass
6. 5.

   Using the two traces, how do their frequencies compare, Pia?

   • They are equal, since both are springs
   • A's is twice B's: 1 Hz and 0.5 Hz
   • B's is twice A's: 1 Hz and 0.5 Hz
7. 6.

   The two masses in the traces are equal. Which spring is stiffer, Ren?

   Use the picture in question 5.

   • A's spring, 4 times as stiff
   • A's spring, 2 times as stiff
   • B's spring, 4 times as stiff
8. 7.

   Which trace shows the greater maximum speed, Tala?

   Use the picture in question 5.

   • They are equal, about 25 cm/s
   • A, since its period is shorter
   • B, since its amplitude is bigger
9. 8.

   A 0.5 kg mass makes the motion in this graph. What is the spring constant, Zee?

   • About 1.6 N/m
   • About 9.9 N/m
   • About 4.9 N/m
10. 9.

    A 2 kg mass on a spring has a period of 0.5 s. What is the spring constant, Ari?

    • About 316 N/m
    • About 25 N/m
    • About 158 N/m
11. 10.

    Which formula gives k from a measured period T and mass m, Bo?

    • k = 2πm ÷ T
    • k = 4π²m ÷ T
    • k = 4π²m ÷ T²