We consider a bead of mass m, being subject to the force of gravity, F, =...

  

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We consider a bead of mass m, being subject to the force of gravity, F, = mgê,, gliding without friction on a stick whose angle o is increasing linearly with time, Le., Bead gliding on a stick O= o(t) = at. (a) Determine the Lagrange funetion in terms of the generalized coordinate I. (1 pt.) (b) Derive the equation of motion for 1(t). (1 pt.) (e) Find the general solution for fit). (2 pts.) (d) Initially, the bead is held fixed at distance lo and released at t = 0, Solve the exquation of motion for this initial condition. (1 pt.) (e) Discuss the solution of part (d) for small times, ie, for at « 1. (Hint: use a Taylor expansion up to second order, i.e, up tofat). (1 pt.) We consider a bead of mass m, being subject to the force of gravity, F, = mgê,, gliding without friction on a stick whose angle o is increasing linearly with time, Le., Bead gliding on a stick O= o(t) = at. (a) Determine the Lagrange funetion in terms of the generalized coordinate I. (1 pt.) (b) Derive the equation of motion for 1(t). (1 pt.) (e) Find the general solution for fit). (2 pts.) (d) Initially, the bead is held fixed at distance lo and released at t = 0, Solve the exquation of motion for this initial condition. (1 pt.) (e) Discuss the solution of part (d) for small times, ie, for at « 1. (Hint: use a Taylor expansion up to second order, i.e, up tofat). (1 pt.)