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A vibrating system has weight W = 4000 lb and a spring stiffness coefficient k = 10,000 lb/in. It has been determined experimentally that the logarithmic decrement Δ = 0.314 and the time between successive maximum Td = 0.2025s for the system.
Determine the following for the system in the given units:
a) The natural undamped frequency (rad/s)
b) The critical damping (lb · s/in)
c) The damping coefficient (lb · s/in)
d) The number of cycles and the time (s) required for the amplitude of motion to be reduced from an initial value of 0.1 in to 0.01 in. Hint: use log properties and the ratios of successive peak amplitudes.
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Find the constant which include with equation after integral - complete elliptic integrals of the first and second kind.
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Copy machine maintenance may be $500 for the first year and will increase by $100 each year. Evaluate if it is worth buying at an interest rate of 6%?
Use your result from part (b) to determine all of the points at which the graph of x = y5 - 5y3 + 4y has a vertical tangent line. Use implicit differentiation to find a formula for dy/dx.
A stained-glass window in a church is designed to be in the area between y is equal to negative x raised to the fourth power pluss 4096 and y is equal to zero (dimensions in feet). What is the area of the window?
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