jennyderath12
29.04.2021 •
Physics
4. When one uses a magnifying glass to view an magnifying glass to view an object, one is using a??
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Ответ:
the value for the damping constant is c = 5.3408Ns/m and the spring constant is k is 987N/m
Explanation:
Consider the formula for the logarithmic decrement (δ)
δ =
Consider the formula for damping ratio (C)
C =δ / √4π² + ² ----------(2)
The given amplitude of the 30th cycle is 20% amplitude of the 1st cycle
The ratio of last peak to first peak is
%--------------(3)
where
n is the number of cycle
Re arrange eqn (3)
The given value for n is 30
substitute 30 for n and eqn (4) in eqn(1)
δ =
substitute 0.0536 for δ in eqn (2)
Consider the formula for damping ratio (C)
C =
where
c is the damping constant
m is the mass
substitute 100 for m in eqn(6)
compute eqn(5) and eqn(7)
The given time to complete 30 cycles in 60s is
period = 60 / 30
= 2s
Formula for spring constant
where
is the undamped natural frequency
consider the formula for damped natural frequency
rearrange
substitute eqn (10) to eqn (9)
consider the formula for the damped natural frequency
consider eqn (12) in eqn (11)
substitute 100 for m, 2 for P, 0.0085 for C in the eqn above
substitute 987 for k in eqn (8)
Thus, the value for the damping constant is c = 5.3408Ns/m and the spring constant is k is 987N/m