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How is the period (T) of a mass-spring system related to mass (m) and spring constant (k)?
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T = 2π (m/k)^{0.5}
What are the characteristics of undamped oscillations in a mass-spring system?
Oscillations continue indefinitely in the absence of friction.
Why does the restoring force in Hooke's Law have a negative sign?
The negative sign indicates that the restoring force is always directed opposite to the displacement.
What happens to the amplitude of damped oscillations over time?
The amplitude decreases over time due to friction.
How does increasing the mass (m) in a mass-spring system affect the period (T)?
Increasing the mass increases the period.
What equation defines the frequency (f) of a mass-spring system?
f = 1/T
What is the equation for the position of a mass in simple harmonic motion (SHM)?
x = A cos(ωt)
In SHM, what is the relationship between angular frequency (ω) and frequency (f)?
ω = 2πf
Given a spring constant k = 100 N/m, calculate the force required to stretch the spring by 0.5 meters.
F = k * x = 100 N/m * 0.5 m = 50 N
What is the formula for the total mechanical energy (ME) in a mass-spring system?
ME = KE + PE
What is the formula for calculating the maximum velocity (v_max) of a mass in SHM?
v_max = (k/m)^{0.5} * A
How do you calculate the work required to stretch a spring?
W = 0.5 kx²
What does the spring constant (k) measure in a mass-spring system?
The stiffness of the spring.
How is kinetic energy (KE) in a mass-spring system at equilibrium position expressed?
KE = 0.5 mv²
Describe what happens at the equilibrium position in a mass-spring system.
Velocity is maximum, restoring force, and acceleration are zero.
What is the maximum acceleration (a_max) formula in SHM?
a_max = (k/m) * A
What type of damping returns to equilibrium without overshooting?
Critical damping.
In a mass-spring system, when is the potential energy (U) at its maximum?
When the spring is fully stretched or fully compressed.
What is resonance in the context of harmonic motion?
Resonance occurs when the applied force frequency matches the system’s natural frequency, maximizing amplitude.
What is the restoring force in a mass-spring system described by?
F_restore = -kx
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