\APPLICATIONS OF SHM

1. Applications of

6. Variation of acceleration with time Displacement is given by: Velocity is given by differentiating the above equation once: Angular Frequency: Differentiating once more gives us the acceleration: On Simplifying:

8. Mass on a pendulum The above formula is used to express the time period of an ideal pendulum system: L is the length of the pendulum and g is the acceleration due to gravity. This shows that the period of oscillation is independent of both the amplitude and pendulum mass.

9. Mass on a spring

11. A mass M attached to a spring of spring constant k exhibits simple harmonic motion in space with: Even the formula on the left can be used to calculate the Time period and hence shows that the period of oscillation is independent of both the amplitude and gravity. The total energy is constant which is given by:

12. Given mass M attached to a spring pendulum with amplitude A with acceleration a : k is the spring constant M is the mass a is the acceleration A is the amplitude OR λ is the wavelength f is the frequency T s or T p is the period of the spring or pendulum g is the acceleration due to gravity is the length of the pendulum E tot is the total energy

15. Some useful and everyday examples are: a mass attached to a spring, a molecule inside a solid, a car stuck in a ditch being “rocked out”, a pendulum, an electron inside an atom .

17. simple harmonic motion is an effect taking place throughout nature which has many practical applications for human beings.

19. Simple harmonic motion spares no one - ranging from the electron inside an atom to the earth rotating around the sun.

20. 2008-09