A block of mass m = 320 g is fastened to a light spring whose force constant 𝑘𝐻 is 72 N/m. The block is pulled a distance 𝑥𝑖= 50 cm from its equilibrium position at x = 0 on a horizontal frictionless surface and released at t =0. (a) What is the mechanical energy of the oscillating block? (b) What is the maximum speed of the oscillating block? (c) Find the velocity, kinetic energy, and potential energy of the block when its position is 30 cm? What Is Simple Harmonic Motion? A Simple Harmonic Motion, or SHM, is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The direction of this restoring force is always towards the mean position. The acceleration of a particle executing simple harmonic motion is given by a(t) = -ω2 x(t). Here, ω is the angular velocity of the particle. Simple Harmonic, Periodic and Oscillation Motion Simple harmonic motion can be described as an oscillatory motion in which the acceleration of the particle at any position is directly proportional to the displacement from the mean position. It is a special case of oscillatory motion. All the Simple Harmonic Motions are oscillatory and also periodic, but not all oscillatory motions are SHM. Oscillatory motion is also called the harmonic motion of all the oscillatory motions, wherein the most important one is Simple Harmonic Motion (SHM). In this type of oscillatory motion, displacement, velocity and acceleration, and force vary (w.r.t time) in a way that can be described by either sine (or) the cosine functions collectively called sinusoids. Difference between Periodic, Oscillation and Simple Harmonic Motion Periodic Motion A motion repeats itself after an equal interval of time. For example, uniform circular motion. There is no equilibrium position. There is no restoring force. There is no stable equilibrium position. Oscillation Motion To and fro motion of a particle about a mean position is called an oscillatory motion in which a particle moves on either side of the equilibrium (or) mean position is an oscillatory motion. It is a kind of periodic motion bounded between two extreme points. For example, the oscillation of a simple pendulum, spring-mass system. The object will keep on moving between two extreme points about a fixed point is called the mean position (or) equilibrium position along any path (the path is not a constraint). There will be a restoring force directed towards the equilibrium position (or) mean position. In an oscillatory motion, the net force on the particle is zero at the mean position. The mean position is a stable equilibrium position. Simple Harmonic Motion or SHM It is a special case of oscillation, along with a straight line between the two extreme points (the path of SHM is a constraint). The path of the object needs to be a straight line. There will be a restoring force directed towards the equilibrium position (or) mean position. The mean position in Simple Harmonic Motion is a stable equilibrium. Conditions for SHM Types of Simple Harmonic Motion The SHM, or Simple Harmonic Motion, can be classified into two types: Linear SHM Angular SHM Linear Simple Harmonic Motion When a particle moves to and fro about a fixed point (called equilibrium position) along with a straight line, then its motion is called linear Simple Harmonic Motion. For example, the spring-mass system. Conditions for Linear SHM The restoring force or acceleration acting on the particle should always be proportional to the displacement of the particle and directed towards the equilibrium position. Angular Simple Harmonic Motion When a system oscillates angular long with respect to a fixed axis, then its motion is called angular simple harmonic motion. Conditions to Execute Angular SHM The restoring torque (or) angular acceleration acting on the particle should always be proportional to the angular displacement of the particle and directed towards the equilibrium position. ----------------------------------------------------------- Subscribe to the channel here: https://youtube.com/@iqinitiative Email: iqinitiative2020@gmail.com Facebook: https://www.facebook.com/profile.php?id=100075842837411&mibextid=ZbWKwL Tweeter: https://twitter.com/IQ_Initiative?t=bdygiJlluZqa_1CxLEuEJA&s=09 Τ ∝ θ or α ∝ θ Where, Τ – Torque α – Angular acceleration θ – Angular displacement