I'm confused about Simple Harmonic motion in physics, please help?

1) A body oscillates with simple harmonic motion along the x-axis. Its displacement varies with time according to the equation x = 5sin(πt +π/3). The phase (in radians) of the motion at t = 2 seconds is...?

I'm very confused because I thought that the equation for displacement x is x = Acos(ωt + ϕ)... it doesn't have sine in it... The equation for velocity does (v = -ωAsin(ωt)) but the question clearly states the expression is for displacement, not velocity...

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2) The motion of a particle is described by x = 5 sin(πt + πi/3). The velocity (in m/s) of the body at t = 1 second is...?

What is the "i" in the equation supposed to mean? Does it indicate direction? Why would that be important to the problem? I'm not sure what to do with this question either... I'm very confused. Please help.

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  • 1 decade ago
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    1) φ=πt+π/3

    t=2 s ==> φ=2π+π/3=7π/3 rad

    2) "i" is a mistake

    If x=5sin(πt+π/3) m, then

    v=x'=5πcos(πt+π/3)

    t=1 s ==>

    v=5πcos(π+π/3)=5πcos(4π/3)=

    5π*(-1/2)=-5π/2 m/s

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