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Simple harmonic motion equations derivation?
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[QUOTE="Tanya Sharma, post: 4581557, member: 434875"] If there is no friction or dissipation,kinetic and potential energy are alternately transformed into each other in SHM,but the total mechanical energy E=K+U is conserved. Consider a spring with one end attached to the wall and other end having a block,going through its cycle of oscillation. Total energy E = (1/2)mv[SUP]2[/SUP] + (1/2)kx[SUP]2[/SUP] At any position x, E = (1/2)mv[SUB]x[/SUB][SUP]2[/SUP] + (1/2)kx[SUP]2[/SUP] At the extreme position ,i.e at x=A the block has only potential energy ,so E = (1/2)kA[SUP]2[/SUP] At the equilibrium position ,at x=0 the block has only kinetic energy ,so E = (1/2)mv[SUB]max[/SUB][SUP]2[/SUP] Now we know,v[SUB]max[/SUB] = ωA ,so at x=0 E=(1/2)mω[SUP]2[/SUP]A[SUP]2[/SUP] [/QUOTE]
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Simple harmonic motion equations derivation?
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