A mass of 0.500 kg is attached to a spring and set into oscillation on a horizon

Question

A mass of 0.500 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by

x(t) = (0.760 m)cos[(16.0 rad/s)t].

Determine the following.

2. 0.61 points | Previous Answers OSUniPhys1 15.1.WA.010.Tutorial My Notes Ask Your Teacher 0 A mass of 0.500 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) (0.760 m)cos16.0 rad/s)t]. Determine the following (a) amplitude of oscillation for the oscillating mass 0.760 rm (b) force constant for the spring 128 N/m (c) position of the mass after it has been oscillating for one half a period 0.76 mi (d) position of the mass one-third of a period after it has been released 0.759 How can you determine the position of the object at a specific time from an expression for the position of the object at any time? m (e) time it takes the mass to get to the position x-0.100 m after it has been released 16.3 How can you determine the time for the oscillating mass to get to a specific position from an expression for the position of the object at any time?s

Explanation / Answer

a) A = 0.760 m

b) k = 16²*0.5 = 128 N/m

T = 2pi*sqrt[m/k] = 0.3927 sec; ½T = 0.1963 sec; ?T = 0.1309 sec

c) x = 0.760 * cos (16*0.1963) = -0.76 m

d) x = 0.760 * cos (16*0.1309) = -0.38 m

e) -0.10 = 0.76*cos(16*t) ? t = 0.106 sec

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