A mass sits between two springs, both at their natural length. The block rests on a frictionless, horizontal desk. a) If I displace the mass by ∆x to the right, draw a Free Body Diagram of the forces now felt by the mass. b) Write Newton’s 2nd Law for this case and decompose the directions until you can write one of the equations as as = −ω2s. Determine what s and ω must be c) From this, prove the angular period of the mass is T = 2π sq root m / k1 + k2 and write x(t) of the spring d) If I begin the motion by displacing a mass of 4kg by 12.5cm, draw a graph of the mass’s motion if k1 = 100N/m and k2 = 200N/m with as many labels as possible
A mass sits between two springs, both at their natural length. The block rests on a
frictionless, horizontal desk.
a) If I displace the mass by ∆x to the right, draw a Free Body Diagram of the
forces now felt by the mass.
b) Write Newton’s 2nd Law for this case and decompose the directions until you
can write one of the equations as as = −ω2s. Determine what s and ω must be
c) From this, prove the angular period of the mass is T = 2π sq root m / k1 + k2 and write x(t) of the spring
d) If I begin the motion by displacing a mass of 4kg by 12.5cm, draw a graph of
the mass’s motion if k1 = 100N/m and k2 = 200N/m with as many labels as possible
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d) If I begin the motion by displacing a mass of 4kg by 12.5cm, draw a graph of
the mass’s motion if k1 = 100N/m and k2 = 200N/m with as many labels as possible
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