3) A 3 kg mass is attached to the end of a horizontal spring, with k = 1500 N/m. The mass is pulled out to x= 2 m from its equilibrium position, then let go. Assume the surface is frictionless, k= 1500 N/m X₁ = 2 m a) What is the spring force before it is released and the acceleration immediately after it is released? - 300 F. =_ 1500(2) 300/3 b) What are each of the following before the mass is released? 30 PEP N PE, p = E₁ = 30 30+0=30 ½(1500) (-2)² e) What are each of the following as the mass passes through the equilibrium position, x = 0? Some of these will be in terms of variables. O J. Vm= wxm a = 100 KE, = m = 3 kg -5 (3)(0) J. KE = 1.5veg ² J. -5(3)veq² d) Using conservation of energy, find the speed of the mass as it passes through equilibrium x = 0. 4.47 Celana Park of 2 •Sveq² =30 e) What are the frequencies and period of the motion? 1=3.56 veg²-20=√√√20 = 4.47 217 J. = 22.36 rad/sec JK --√√1500 22.36 277=6.28 3 f) What are maximum values of the velocity and acceleration? These should be familiar. 100 m/s² am E = Hz 1.5 veg². =Wvm T= 0.281 sec. 7/-3/56 =
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
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