A particle of mass m moves along a trajectory given by x = a cos delta 1, t and y = a sin ...

Question:

A particle of mass {eq}m {/eq} moves along a trajectory given by {eq}x = a \cos \delta 1\, t {/eq} and {eq}y = a \sin \delta 2\, t {/eq}.

Find {eq}r {/eq} and {eq}y {/eq} component of the force acting on the particle, potential energy, kinetic energy of the particle and hence show that the total energy {eq}E = KE + PE =1/2 m(a \ast 2\, \delta 1 \ast 2 + b\ast 2 \, \delta 2 \ast 2) {/eq}

Spring-Mass System

The spring-mass system is formed by a mass {eq}m {/eq} attached to a spring with elastic constant {eq}k {/eq}. The system undergoes a simple harmonic motion whose frequency equals,

{eq}\omega=\sqrt{\dfrac{k}{m}} {/eq}.

The mechanical energy is conserved shifting from kinetic energy of the body to elastic potential of the spring,

{eq}E=K+E_{ep}=\dfrac{1}{2}kA^2 {/eq},

where {eq}A {/eq} is the motion's amplitude, the maximum deformation of the mass from its equilibrium position.

Answer and Explanation:

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We are given:

{eq}\bullet \; x=a\cos(\delta_1 t) {/eq}, the law of motion for the x-coordinate of the mass.

{eq}\bullet \; y=a\cos(\delta_2...

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Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.


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