A particle of mass m = 0.5 kg attached to a spring executes simple harmonic motion. It begins at rest from Xo = +25 cm and oscillates about its equilibrium position at x = 0 with a period of 1.5 s. Write equations for: a. the position x(t) as a function of time; b. the velocity v(t) as a function of time; C. the acceleration a(t) as a function of time; d. the restoring force of the spring, in terms of x(t). Assume now that the same particle above instead has initial conditions of xo = +25 cm and vo = +50 cm/s. Calculate now: e. the phase constant and the amplitude; f. the total energy of the mass/spring system; g. the kinetic energy and the potential energy of the system initially and show that their sum equals the result in part (f).
A particle of mass m = 0.5 kg attached to a spring executes simple harmonic motion. It begins at rest from Xo = +25 cm and oscillates about its equilibrium position at x = 0 with a period of 1.5 s. Write equations for: a. the position x(t) as a function of time; b. the velocity v(t) as a function of time; C. the acceleration a(t) as a function of time; d. the restoring force of the spring, in terms of x(t). Assume now that the same particle above instead has initial conditions of xo = +25 cm and vo = +50 cm/s. Calculate now: e. the phase constant and the amplitude; f. the total energy of the mass/spring system; g. the kinetic energy and the potential energy of the system initially and show that their sum equals the result in part (f).
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Just do part e) please, and provide a clear explanation, thanks.
Transcribed Image Text:A particle of mass m = 0.5 kg attached to a spring executes simple harmonic motion. It begins at rest from
Xo = +25 cm and oscillates about its equilibrium position at x = 0 with a period of 1.5 s. Write equations
for:
a. the position x(t) as a function of time;
b. the velocity v(t) as a function of time;
C. the acceleration a(t) as a function of time;
d. the restoring force of the spring, in terms of x(t).
Assume now that the same particle above instead has initial conditions of xo = +25 cm and vo = +50
cm/s. Calculate now:
e. the phase constant and the amplitude;
f. the total energy of the mass/spring system;
g. the kinetic energy and the potential energy of the system initially and show that their sum equals
the result in part (f).
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