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Unformatted text preview: Lesson 44: Acceleration, Velocity, and Period in SHM Since there is a restoring force acting on objects in SHM it makes sense that the object will accelerate. In Physics 20 you are only required to explain this acceleration for masses on horizontal springs with no friction, and basic pendulums. Vertical springs will not be covered here. Acceleration of a Mass on a Spring As a mass bounces back and forth on a spring, it will have a changing acceleration. The changing acceleration happens because the restoring force is always changing. As long as the situation is frictionless, there are no other forces to consider, so the net force will be the restoring force. F NET = F s ma = kx a = kx m Example 1 : Determine the acceleration of a 0.250kg mass on the end of a 54.9N/m spring if it has been... a) stretched 12cm from its equilibrium and released. b) compressed 25cm from its equilibrium and released. a) a = kx m a = 54.9 0.12 0.250 a = 26 m / s 2 b) a = kx m a = 54.9 0.25 0.250 a = 55 m / s 2 These answers are the acceleration at that moment. An instant later (when they have moved to a different position) their accelerations will be different. The answer in (a) is negative because the spring has been stretched; the mass is trying to accelerate in the opposite direction back to equilibrium. In (b) the answer is positive because the object was compressed and the mass is trying to accelerate back in the positive direction to equilibrium. 1/5/2007 studyphysics.ca Page 1 of 5 / Section 7.3 acceleration acceleration Illustration 1: Mass undergoing acceleration. Velocity of a Mass on a Spring Some people think that a big acceleration automatically means that the object is moving at a big velocity. Remember that in the examples above the mass has just been released from rest, so its velocity starts at zero....
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