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Unformatted text preview: 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 = 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 ( t + 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, , and 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 seconds for the block to travel 40 cm, so the initial speed v o can be found by dividing 40 cm by 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 = sec: At maximum displacement 500 g + x v o 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 away from ( e.g., to the right of) equilibrium. .b Determine an expression (in terms of m, g, and ) for the component of the net force on the bob that points tangent to the path of the bob....
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