How Does Energy Impact Bridge Oscillation Amplitudes?

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CMATT
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A suspension bridge oscillates with an effective force constant of
Equation: 1.120 x 10^8
N/m.

(a) How much energy is needed to make it oscillate with an amplitude of 0.106 m?

(b) If soldiers march across the bridge with a cadence equal to the bridge's natural frequency and impart
Scientific notation showing 1.200 × 10^4.
J of energy each second, how many minutes does it take for the bridge's oscillations to go from 0.106 m to 0.530 m amplitude, assuming the bridge has no damping?

RELEVANT EQUATIONS:
For (a)
Etot = (.05)(k)(xmax)^2

For (b)
not sure

THE ATTEMPT AT THE SOLUTION:

a)
k = 1.120E8 N/m
xmax^2 = .106 m

Etot = (.05)(k)(xmax)^2 = (.05)(1.120E8)(.106) = 6.29E5 J
This answer was correct on my webassign

b) I'm very confused here. All I know is 6.29E5 J is the energy required to make it oscillate with an amplitude of .106 m
 
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CMATT said:
A suspension bridge oscillates with an effective force constant of
Equation 1.120 × 10^8 in scientific notation, shown as a small standalone expression.
N/m.

(a) How much energy is needed to make it oscillate with an amplitude of 0.106 m?

(b) If soldiers march across the bridge with a cadence equal to the bridge's natural frequency and impart
Small rendered expression reading 1.200 × 10^4, a number in scientific notation.
J of energy each second, how many minutes does it take for the bridge's oscillations to go from 0.106 m to 0.530 m amplitude, assuming the bridge has no damping?

RELEVANT EQUATIONS:
For (a)
Etot = (.05)(k)(xmax)^2

For (b)
not sure

THE ATTEMPT AT THE SOLUTION:

a)
k = 1.120E8 N/m
xmax^2 = .106 m

Etot = (.05)(k)(xmax)^2 = (.05)(1.120E8)(.106) = 6.29E5 J
This answer was correct on my webassign

b) I'm very confused here. All I know is 6.29E5 J is the energy required to make it oscillate with an amplitude of .106 m

What is the energy when the bridge oscillates with 0.530 m amplitude?
The soldiers impart
Small rendered equation reading 1.200 x 10^4, showing a decimal value of 1.200 multiplied by ten raised to the fourth power.
J of energy each second
to the bridge. How long time is needed that the bridge get the new energy?
 
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