Chapter 13: Simple Harmonic Motion and Hooke’s Law and using back to back on the photocopier. Please remember to photocopy 4 pages onto one sheet by going A3→A4 Hooke’s Law states that when a force is needed to extend or compress a spring by some distance, the restoring force Hooke’s Law is proportional to the displacement. We represent this mathematically as follows; F - extension* that the restoring force and the extension (or compression) are opposite in direction. The “minus’ signifies The most common example of is a stretched string. Hooke’s Law Simple Harmonic Motion (S.H.M.)* An object is said to be moving with Simple Harmonic Motion if; its acceleration is directly proportional to its displacement a fixed point in its path, and from its acceleration is directed that point. towards We represent this mathematically as : The to in the definition is also called the ‘fixed point’ referred ‘equilibrium position’. The key to SHM is that the acceleration and the displacement are always opposite in direction. This is represented by the minus sign in the equation, although mathematically the minus sign has no significance and can be ignored for calculations. represented angular “But I thought ω velocity?”* Other examples of SHM, apart from a stretched string are: A prong on a vibrating tuning fork A pendulum oscillating at a small angle To show that any object that obeys will also execute SHM Hooke’s Law The aim here is to show that is a subset of S.H.M., i.e. that F -s can be rewritten in the form a = - 2 s. Hooke’s Law So we start with the equation for Law; F -s F = -k s Hooke’s But F = ma ma = -k s Now divide both sides by m Comparing the equation to the general expression for simple harmonic motion we can equate to get or This relationship is used in all the long exam questions below Relationship between Periodic Time (T) and for an object undergoing SHM* As with waves, the periodic time is the time taken for one complete oscillation. Also T = 1/f, where f is the frequency. Remember is not angular velocity. What is the unit of in this particular case? Answering the long maths questions
Chapter 13: Simple Harmonic Motion and Hooke’s Law Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier. Hooke’s Law Hooke’s Law states that when a force is needed to extend or compress a spring by some distance, the restoring force is proportional to the displacement. We represent this mathematically as follows; F - extension* The “minus’ signifies that the restoring force and the extension (or compression) are opposite in direction. The most common example of Hooke’s Law is a stretched string. Simple Harmonic Motion (S.H.M.)* An object is said to be moving with Simple Harmonic Motion if; its acceleration is directly proportional to its displacement from a fixed point in its path, and its acceleration is directed towards that point. We represent this mathematically as : The ‘fixed point’ referred to in the definition is also called the ‘equilibrium position’. The key to SHM is that the acceleration and the displacement are always opposite in direction. This is represented by the minus sign in the equation, although mathematically the minus sign has no significance and can be ignored for calculations. “But I thought ω represented angular velocity?”* Other examples of SHM, apart from a stretched string are: A prong on a vibrating tuning fork A pendulum oscillating at a small angle To show that any object that obeys Hooke’s Law will also execute SHM The aim here is to show that Hooke’s Law is a subset of S.H.M., i.e. that F -s can be rewritten in the form a = - 2 s. So we start with the equation for Hooke’s Law; F -s F = -k s But F = ma ma = -k s Now divide both sides by m Comparing the equation to the general expression for simple harmonic motion we can equate to get or This relationship is used in all the long exam questions below Relationship between Periodic Time (T) and for an object undergoing SHM* As with waves, the periodic time is the time taken for one complete oscillation. Also T = 1/f, where f is the frequency. Remember is not angular velocity. What is the unit of in this particular case? Answering the long maths questions
13.%20Hookes%20Law%20and%20SHM.docx