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Sagot :
The total energy E of the object-spring system is 0.0648m Joules
We know that,
The total energy E = 1/2 * Mass m * Angular frequency ω * Amplitude A
The maximum acceleration a = [tex]w^{2}[/tex] * Amplitude A
Given,
Amplitude A = 12cm
The maximum acceleration a = 108 cm/s2
a = [tex]w^{2}[/tex] * A
108 = [tex]w^{2}[/tex] * 12
ω = 3 [tex]s^{-1}[/tex]
The Energy needs to be in Joules. So,
Joules = kg * [tex]m^{2}[/tex] / [tex]s^{2}[/tex]
ω * A = 36 cm / s = 0.1296 [tex]m^{2}[/tex] / [tex]s^{2}[/tex]
E = ½ * m * 0.1296
E = 0.0648m Joules (where m is in Kg).
The total energy E of the object-spring system is the sum of potential energy and kinetic energy.
Therefore the total energy E of the object-spring system is 0.0648m Joules
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