a mass-spring-damper system has a mass of 100 kg. its free response amplitude decays such that the am- plitude of the 31st cycle is 20% of the amplitude of the 1st cycle. the system takes 60 seconds to complete 30 cycles. estimate the damping constant c and the spring constant k.

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10-11-2022
Physics

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a mass-spring-damper system has a mass of 100 kg. its free response amplitude decays such that the am- plitude of the 31st cycle is 20% of the amplitude of the 1st cycle. the system takes 60 seconds to complete 30 cycles. estimate the damping constant c and the spring constant k.

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rekharaypriti8910 rekharaypriti8910 · Answer 1 · 2022-11-16T01:22:16-05:00

The oscillator's mass (m) and stiffness (k) are used to calculate the critical damping coefficient (cc) using the following formula: cc = 2(km).

The mass is increased to the starting amplitude position A0 before being let go. In a fluid with viscosity, the mass oscillates about the equilibrium position, but the amplitude gets smaller with each oscillation. According to this website, the formula for the damping force,

Fd, is Fd=-cv,

=100 * 60/30

=600

where c stands for the damping coefficient and v for the velocity. According to Hooke's Law, a spring's force is proportional to how far it has moved from its rest position. Where F is the force applied by the spring, F = -k * x x

is the displacement of the spring from rest in meters, and k is the "spring constant."

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