A particle of mass m undergoes one-dimensional undamped harmonic oscillation due to a restoring force Fr = -kx. In addition the particle is subject to a constant external force Fext = Fo.(adsbygoogle = window.adsbygoogle || []).push({});

a) What is the differential equation that governs the motion of the particle?

b) what is the general solution for the position of the particle as a fxn of t?

c) What is the motion of the particle in the limit t - > infinity

d) If the oscillations are damped, what would be the motion of the particle in the limit t-> infinit?

a) d^2x/d^t^2 + kx/m = Fo/m

b) After applying the method of undetermined coefficients

x(t) = Acos(Wot + phi) + Fo/k

c) V = -Asin(Wot+ phi)(Wo)

t-> infiity , v - inifity?

d) If the former was undamped, how does introducing the damping constant change my solution?

Thanks

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# One-dimensional undamped harmonic oscillation

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