Problem 4.6 Obtain the equations of motion for a spherical pendulum, that is, a pendulum that is not constrained to oscillate in a plane.
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- What is the period of oscillation (in seconds) of a rod of length 4.43m that is fixed at one end, but otherwise free to rotate without any friction, which has a mass 4.78kg, for small displacements? Note: In the space below, please enter you numerical answer. Do not enter any units. If you enter units, your answer will be marked as incorrect.Calculate the constants b₁ and b2 in the the following equation 1 Imax d²x(t) for the condition (0) ) = xmax, the maximum extension of the oscillator. What is v(0) for this condition? Match the items in the left column to the appropriate blanks in the equations on the right. Make certain each equation is complete before submitting your answer. ?). dt² ∞ b₂ 0 t=0 dx (t) (da)₁-0 dt t=0 b₁ x(t) v(0) = xmax = b₁ co Therefore, b₁ = 0 + b₂ sin and b₂ = (√5.0) k μl • (√) +0 k COS 00 (√5-0) x(t) = b₁ cos Reset t + b₂ sin 2 sin (√) HelpThe system in the figure below is in equilibrium, and its free body diagram drawn on the right. The distance, d is 1.14 m and each of the identical spring's relaxed length is l0 = 0.57 m. The mass, m of 0.86 kg brings the point P down to a height h = 15 cm. The mass of the springs are negligible. Calculate the following quantities: (a) The angle ? (b) The force exerted on P by the right spring (c) The force exerted on P by the left spring (d) The total spring length (e) The stretch length (f) The stiffness constant of the springs