Examples of SHM

• When a mass on a spring is displaced from its equilibrium position and released, it will oscillate with Simple Harmonic Motion (SHM).
• The tension in the spring and the weight of the object cause an acceleration which always acts towards the equilibrium position.
• Understanding of Hooke’s law allows us to calculate the tension in the spring as ke where e is the extension of the spring and k is the spring constant.
• The resultant force of the tension and weight can be used to calculate the acceleration using F=ma where m is the mass of the object.
• The equation for the acceleration of the object is a=-mkx.
• Both k and m are constant, making the equation for SHM a=-w2x=-mkx.
• The equation for the period of oscillation can be given as T=2πkm.
• Using the small angle approximation, the acceleration of the bob is given by a=-lgx.
• Comparing this to the SHM equation a=-ω2x gives the following equation for the period of oscillation of the pendulum: T=2πgl.