Question

A cart of mass 260 g is placed on a frictionless horizontal air track. A spring having a spring constant of 8.0 N/m is attached between the cart and the left end of the track. The cart is displaced 3.5 cm from its equilibrium position.

(a) Find the period at which it oscillates.
   s

(b) Find its maximum speed.
   m/s

(c) Find its speed when it is located 2.0 cm from its equilibrium position.
  m/s

Answer 1

Solution)

Given,

Mass, m=0.26 kg

Spring constant, K=8 N/m

Amplitude, A=0.035 m

Angular frequency, w=root(k/m)=root(8/0.26)=5.54 rad/s

Part a)

Time Period, T=2pi/w= 2pi/5.54= 1.13 sec (Ans)

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Part b)

Maximum speed, v= A*w=0.035*5.54= 0.1939 m/s (Ans)

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Part c)

Displacement, x=3.5-2=1.5 cm=0.015 m

Now, speed, v'= w*sqrt(A^2-x^2)

V'=5.54*sqrt(0.035^2-0.015^2)= 0.175 m/s (Ans)

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