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Simple Harmonic motion of particle on a table

  1. Jan 2, 2005 #1
    1. A particle mass attached to one end of a light spring is executing SHM on a smooth horizontal table. If another identical particle is attached to the other end of the spring, what is the period of oscillation?

    I don't know how to figure this problem out....I used to deal with a spring fixed to the wall only....please help!!

    2. A pendulum is set to swing with an amplitude of 4cm and a period of 0.8s. The mass of the pendulum bob is 0.5kg. Calculate the tension in the string when the bob is at the lowest position.

    I set the equation as: F = T-mg, as F is net force pointing towards the centre, T is tension.........T= F+mg.....T= mv^2/r + mg.....T = m(w^2 *A + g)........T = 0.5 ( (2pi/0.8)^2 *0.004 + 10)........T = 6.23N
    But it is wrong...can anyone tell me why?

    3. When a ball hits the ground, acceleration-time graph <a> is drawn....and if some kinetic energy is lost, that means the ime for the upward flight decreases. another acceleration-time graph <b> is drawn...But why <a> and <b> is the same? I suppose for graph <b>, the time duration in the rebounce( contaction with the ground) is longer, isn't it?

    Any help would be appreciated.
     
    Last edited: Jan 3, 2005
  2. jcsd
  3. Jan 3, 2005 #2
    For number 2:
    F = T-mg... I think there is something wrong in this formula. My apologies if I'm wrong, but I think that when the bob is at its lowest point, the bob doesn't move vertically. So, I think that the net vertical force should be zero, hence:

    total upward forces = total downward forces
    => Tension(T) + Centripetal_force(F) = Weight(W)
    => T + F = w
    => T = W - F
    => T = mg - ma

    but we know that the acceleration(a) = (v^2)/r , where v is the velocity at the bottom and r simply the amplitude.

    But, its better to use a = r (w^2) , where w(omega) is [ (2*PI)/T ], where T is the period.

    So, if you just replace, you will have: -

    => T = mg - ma
    => T = m(g - a)
    => T = m(g - r ( w^2) )

    and hence,
    => T = m [ g - r ( ((2*PI)/T)^2)]............(sorry, I don't know how to use latex yet :)

    I got 3.76N as answer to 3 S.F
     
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