Spring Pendulum(Vertical)


This simulation ignored the effects of friction.

Simple harmonic oscillation

In everyday life, we see a lot of movements that repeated the same oscillation.
Like below, shaky or suspended objects are doing this oscillation.

  1. Clock pendulum
  2. An object suspended in a spring
  3. Swing
  4. musical instruments string
  5. Piston movement of internal combustion engine
  6. Voltage wave of AC power

When the vibrations are based only on restoring forces such as springs, they are called simple harmonic oscillators.

Period and frequency

Frequency is the number of vibrations in 1 second. The frequency is denoted by ‘f,’ and the standard unit is ‘Hz.’

1 Hz = 1 vibration/second = 1 s-1

The period is the time taken to vibrate once. The period is marked as ‘T.’

period(s) × frequency(Hz) = 1

T × f = 1

The period of the spring pendulum is as follows:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]

m: Mass of weight(kg)
k: Spring Constant(N/m)

‘k’ is the spring constant. For example, if you need 1N force to pull 1m of spring, the spring constant is 1N/m, and if you need 2N, it is 2N/m.
In the spring pendulum, the amplitude does not affect the period. In other words, the vibration frequency does not change even if the amplitude is large or small.

We can obtain the frequency (Hz) from the relationship between the period and the frequency.

\[f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \]

Gravity effect for vertical spring scales

When we observe a vertically moving spring, it looks a bit complicated because gravity is interrupted. However, gravity merely shifts the initial position of the weight suspended on the spring balance and does nothing more.
Therefore, you can ignore the effects of gravity when calculating vibrations.