![simple harmonic motion simple harmonic motion](https://d1whtlypfis84e.cloudfront.net/guides/wp-content/uploads/2018/02/19170158/graph.gif)
For a mass on a spring, where the restoring force is F = -kx, this gives: The frequency of the motion for a mass on a springįor SHM, the oscillation frequency depends on the restoring force. We'll look at that for two systems, a mass on a spring, and a pendulum.
![simple harmonic motion simple harmonic motion](http://1.bp.blogspot.com/-RJkSDfVZFoA/UL2k52BWBLI/AAAAAAAAItA/M3vxAJ45vsE/s1600/Figure+4.2+SIMPLE+HARMONIC+MOTION.jpg)
What distinguishes one system from another is what determines the frequency of the motion. The acceleration can in fact be written as:Īll of the equations above, for displacement, velocity, and acceleration as a function of time, apply to any system undergoing simple harmonic motion. Note that the equation for acceleration is similar to the equation for displacement. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force the force applied by the spring is in the opposite direction as the displacement. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. The acceleration also oscillates in simple harmonic motion. It turns out that the velocity is given by:
![simple harmonic motion simple harmonic motion](https://www.researchgate.net/profile/Mahesh-Lohith-K-S/publication/327602134/figure/fig1/AS:670046368043018@1536762911498/Simple-Harmonic-Motion.jpg)
When the displacement is maximum, however, the velocity is zero when the displacement is zero, the velocity is maximum. In simple harmonic motion, the velocity constantly changes, oscillating just as the displacement does. The frequency is how many oscillations there are per second, having units of hertz (Hz) the period is how long it takes to make one oscillation. It is related to the frequency (f) of the motion, and inversely related to the period (T): Note that the in the SHM displacement equation is known as the angular frequency.
![simple harmonic motion simple harmonic motion](https://i.ytimg.com/vi/uM2HpLBVAkA/maxresdefault.jpg)
So, in other words, the same equation applies to the position of an object experiencing simple harmonic motion and one dimension of the position of an object experiencing uniform circular motion. The amplitude is simply the maximum displacement of the object from the equilibrium position. How does this relate to simple harmonic motion? An object experiencing simple harmonic motion is traveling in one dimension, and its one-dimensional motion is given by an equation of the form Plugging this in to the x and y positions makes it clear that these are the equations giving the coordinates of the object at any point in time, assuming the object was at the position x = r on the x-axis at time = 0: The motion is uniform circular motion, meaning that the angular velocity is constant, and the angular displacement is related to the angular velocity by the equation: This is two-dimensional motion, and the x and y position of the object at any time can be found by applying the equations: Consider an object experiencing uniform circular motion, such as a mass sitting on the edge of a rotating turntable. It might seem like we've started a topic that is completely unrelated to what we've done previously however, there is a close connection between circular motion and simple harmonic motion. The connection between uniform circular motion and SHM Simple harmonic motion Simple harmonic motion The object oscillates around the equilibrium position, and the net force on the object is equal to the force provided by the spring. In simple harmonic motion, the acceleration of the system, and therefore the net force, is proportional to the displacement and acts in the opposite direction of the displacement.Ī good example of SHM is an object with mass m attached to a spring on a frictionless surface, as shown in (Figure).