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PHYS310_homework_03 - Homework 3 Simple harmonic motion Due...

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Homework 3: Simple harmonic motion, Due Sept. 14, 11:30 am Name .1 A 500-g block is placed on a level, frictionless surface and attached to an ideal spring. At t = 0 the block moves through the equilibrium position with speed v o in the – x direction, as shown below. At t = π sec, the block reaches its maximum displacement of 40 cm to the left of equilibrium. .a Determine the value of each of the following quantities. Show all work. period: spring constant: .b Using x(t) = A cos ( ϖ t + φ o ) as the solution to the differential equation of motion: Determine the form of the function v (t) that represents the velocity of the block. Evaluate all constant parameters (A, ϖ , and φ o ) so as to completely describe both the position and velocity of the block as functions of time. .c Consider the following statement about the situation described above. "It takes the first π seconds for the block to travel 40 cm, so the initial speed v o can be found by dividing 40 cm by π seconds." Do you agree or disagree with this statement? If so, explain why you agree. If not, explain why you disagree and calculate the initial speed v o of the block. 40 cm t = 0 sec: At equilibrium position t = π sec: At maximum displacement 500 g + x v o
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Homework: Simple harmonic motion .2 A simple pendulum consists of a particle of mass m suspended by a long, massless wire of length L. ( Note: Neglect all frictional effects.) .a Draw a free-body diagram for the pendulum bob corresponding to a moment when the bob is located an angular displacement φ away from ( e.g., to the right of) equilibrium. .b Determine an expression (in terms of m, g, and φ ) for the component of the net force on the bob that points tangent to the path of the bob.
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