7.33 ** A bar of soap (mass m) is at rest on a frictionless rectangular plate that rests on a horizontal table. At time t = 0, I start raising one edge of the plate so that the plate pivots about the opposite edge with constant angular velocity w, and the soap starts to slide toward the downhill edge. Show that the equation of motion for the soap has the form i – w²x = -g sin wt, where x is the soap's distance from the downhill edge. Solve this for x(t), given that x (0) = xo. [You'll need to use the method used to solve Equation (5.48). You can easily solve the homogeneous equation; for a particular solution try x = A sin wt and solve for A.]
7.33 ** A bar of soap (mass m) is at rest on a frictionless rectangular plate that rests on a horizontal table. At time t = 0, I start raising one edge of the plate so that the plate pivots about the opposite edge with constant angular velocity w, and the soap starts to slide toward the downhill edge. Show that the equation of motion for the soap has the form i – w²x = -g sin wt, where x is the soap's distance from the downhill edge. Solve this for x(t), given that x (0) = xo. [You'll need to use the method used to solve Equation (5.48). You can easily solve the homogeneous equation; for a particular solution try x = A sin wt and solve for A.]
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7.33
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![7.33 ** A bar of soap (mass m) is at rest on a frictionless rectangular plate that rests on a horizontal
table. At time t = 0, I start raising one edge of the plate so that the plate pivots about the opposite
edge with constant angular velocity w, and the soap starts to slide toward the downhill edge. Show that
the equation of motion for the soap has the form ï – w?x =-g sin wt, where x is the soap's distance
from the downhill edge. Solve this for x(t), given that x (0) = xo. [You'll need to use the method used
to solve Equation (5.48). You can easily solve the homogeneous equation; for a particular solution try
x = A sin wt and solve for A.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d945e56-c5e1-480a-9c03-390d785d9d79%2Fc000b662-2be9-4f9f-95f8-51c8fbcaa614%2Feq9mae_processed.jpeg&w=3840&q=75)
Transcribed Image Text:7.33 ** A bar of soap (mass m) is at rest on a frictionless rectangular plate that rests on a horizontal
table. At time t = 0, I start raising one edge of the plate so that the plate pivots about the opposite
edge with constant angular velocity w, and the soap starts to slide toward the downhill edge. Show that
the equation of motion for the soap has the form ï – w?x =-g sin wt, where x is the soap's distance
from the downhill edge. Solve this for x(t), given that x (0) = xo. [You'll need to use the method used
to solve Equation (5.48). You can easily solve the homogeneous equation; for a particular solution try
x = A sin wt and solve for A.]
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