The document discusses the energy of a horizontal mass-spring system. It is the sum of the kinetic energy (1/2mv^2) and the elastic potential energy (1/2kx^2). It provides two scenarios: (1) when the spring is expanded, the displacement is positive, and (2) when the spring is compressed, the displacement is negative. In both scenarios, when the mass is released, it accelerates back towards its initial position due to the elastic restoring force of the spring.

1. The total Energyof a horizontal massspringsystemisthe
sumof the kineticenergy(1/2mv^2) andthe elastic
potential energy(1/2kx*2)
KineticEnergy
M = mass of the object
V = velocity
Potential Energy
K = Springconstant
x = displacement
Scenario1 (Expanded/Stretched)
-Workhas beendone tomove frompointA to pointB
-Workthat has beendone toexpandthe springfrom
pointA to B, has beenstoredas elasticpotential energy
-Workdone is = 1/2kx^2
-Displacement(x) ispositive(+) because distancehas
beenaddedfrom the initial position(A)togetto final
position(B)
A
C
Scenario2 (Compressed)
-Workhas beendone tomove frompointA to pointC
-Workthat has beendone tocompressthe springfrom
pointA to C,has beenstoredaselasticpotential energy
-Workdone is = 1/2kx^2
-Displacement(x) isnegative (-)because distance has
beenreducedfromthe initial position(A) togettofinal
position (C)
A
To Summarize:
-Bothworkdone to move the mass fromthe initial tothe final positionisstoredaselasticpotential energyas1/2kx^2
-Displacement(x) ispositiveduringexpansion,because distanceisbeingaddedfromthe initial position
-Displacement(x) isnegative duringcompression,because distance isbeingreducedfromthe initialposition
-Inboth scenarios,whenthe massisreleased,itacceleratesback(eitherdirection) towardsitsinitial position(equilibrium
position).
-Thisisdue to the elasticrestoringforce of the spring
RestoringForce:Whena springisbeingcompressedorstretched(due toforce isappliedtoit) andreturnsback to its
original shape whenthe force isremoved
Learning Objectives –Simple Harmonic Motion
ChristianCebrero,28437144
OSCILLATING:To move backand forth at a regularspeed
C