Oscillations and the Simple Pendulum: Time Period, Frequency, Seconds Pendulum and Spring-Mass

Oscillations: Motion That Repeats Itself

A swing, the bob of a wall clock, a guitar string and a loaded spring all move back and forth about one fixed position. Such motion is called oscillatory motion, and because it repeats after equal intervals of time it is also periodic motion. The fixed position where the body would rest is the mean or equilibrium position.

General-science papers love this topic because a handful of formulas produce many quick questions. The simple pendulum alone gives questions on length, gravity, mass, the Moon, lifts and clocks that gain or lose time. The spring-mass system adds one more formula that behaves differently on the Moon.

The next cards define amplitude, time period and frequency, work through the pendulum and spring formulas with real numbers, and list the traps that examiners set again and again.

1. A body completes one oscillation in 0.25 s. What is its frequency?

2. If the length of a simple pendulum is made four times, its time period:

3. The mass of a simple pendulum's bob is doubled, keeping the length the same. The time period:

4. The length of a seconds pendulum on Earth is approximately:

5. A simple pendulum is taken from the Earth to the Moon. Its time period will:

6. A child sitting on a swing stands up while swinging. The time period of the swing:

7. A 1 kg mass hangs from a spring of spring constant 100 N/m. Its time period is about:

8. A simple pendulum hangs inside a lift whose cable breaks, so the lift falls freely. The pendulum's time period: