Energy & Momentum: Note 4. Simple Harmonic Motion. Simple harmonic motion is a motion that repeats, thus allowing it
Energy & Momentum: Note 4
Simple Harmonic Motion Simple harmonic motion is a motion that repeats, thus allowing it to have a period and a frequency due to its cyclical nature. Lets look at the following example; a mass is connected to the ceiling by a spring. When the mass is held up, the spring is 50.0 cm long. When the mass is released, the spring stretches until some maximum point and pulls the mass back up again. This motion repeats, thus giving the term “harmonic.” As a rule of thumb for SHM questions: -When the system has finished moving and it at rest, use FORCE analysis. -When the system is in motion, use ENERGY analysis. Eg. 1. The mass above (0.750 kg) is released and the spring begins to stretch. When it is at its maximum depth, the spring has stretched 0.240 m. a) Calculate the k-value of this spring (assuming the system is released and at rest. When at rest, x = 0.120 m). b) What is the amount of energy in the system when in SHM? c) What is the velocity of the mass when the spring has stretched 0.180 m?
Energy & Momentum: Note 4 Period and Frequency of a SHM System As mentioned above, the period and frequency can be found for a system in simple harmonic motion. To derive these equations, we need to consider the following scenario:
Derivation: Eg. 2. A 2.50 kg mass is attached to a spring (k = 125 N/m) on a horizontal, frictionless surface. When pulled back x = 25 cm, calculate the period and frequency the system will vibrate at.
