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Simple Harmonic Motion and Springs

Simple Harmonic Motion and Springs. Simple harmonic motion. Starts from a stable point or a rest point When an object is disturbed, it has a restorative force which tries to restore the object to its rest position

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Simple Harmonic Motion and Springs

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  1. Simple Harmonic Motion and Springs

  2. Simple harmonic motion • Starts from a stable point or a rest point • When an object is disturbed, it has a restorative force which tries to restore the object to its rest position • Generally, the force (and therefore) acceleration is proportional to displacement • This results in a back and forth motion that continues indefinitely

  3. Spring Motion • When a spring is stretched and let go, it undergoes a longitudinal motion that is one type of simple harmonic motion. • Restorative Force k – spring constant (N/m) x – displacement (m) • Why would the negative sign be present?

  4. For the purposes of SHM… • We consider an ideal spring… • An ideal spring has no internal or external friction acting upon it • In a practical (unrealistic) sense, this means that spring keeps oscillating forever

  5. If we were to examine the motion wrt time What does this look like? Hint: The answer is not fun. As much fun as it is, that’s not what I’m looking for. What is a sine or cosine function based on?

  6. Let’s see how a unit circle relates to SHM • https://www.geogebratube.org/student/m87292 • How does SHM relate to the unit circle? Observe! • Maximum speed through the rest point • Stopped at the amplitude • f of motion on a point of the circle = f of vibration in SHM • They two motions are in phase • Radius of the circle = amplitude

  7. How can we relate UCM to SHM? • What do we know about things moving in a circle? • Derive

  8. SHM isn’t real life so let’s look at dhm • Damped Harmonic Motion Periodic or repeated motion where amplitude decreases with time There are no perfect springs!!!

  9. Damping of car shocks • Damping for a car’s shocks: - 0.7 is ideal in this case • Overdamping is preferable to underdamping • Why is this so?

  10. Total energy in SHM • Energy is conserved! • Therefore, total energy remains constant • What is types of energy are being exchanged? • - Kinetic for Elastic potential and back • Therefore,

  11. Example • A pendulum is disturbed from rest and is released from an amplitude of 15cm. If the pendulum has a mass of 45g and a spring constant of 26N/m, what will the period of the oscillation be?

  12. Example • A spring (k=20N/m) is compressed 30cm by a ball (m= 100g) and fired upwards. How fast will the object be moving after it has a vertical displacement of 20cm after it leaves the spring?

  13. Review Video • https://www.youtube.com/watch?v=VnGkoMoUkgI

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