Suppose that a mass is attached to two springs in parallel and that the two spri

Question

Suppose that a mass is attached to two springs in parallel and that the two
springs have the same natural length, but possibly di®erent spring constants k1
and k2, respectively.
a. What position of the mass would be called the equilibrium position?
b. Derive a differential equation for this mass-spring system assuming that
there is no resistive force.
c. Show that the mass executes a simple harmonic motion about its equilib-
rium position.
d. What is the period of the oscillation.
e. If the two springs were replaced by one spring, what would be the spring
constant of the new spring such that the motion would be equivalent.

Explanation / Answer

a. x=mg/(k1+k2). b. m*x''+x*(k1+k2)=0. c. above is a 2nd derivative equation. d. T=2pi/w=2pi*sqrt(m/(k1+k2)) e. it should be k=k1+k2

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