All Flashcards
What equation gives the maximum speed in simple harmonic motion?
The maximum speed, vmax, in simple harmonic motion is given by the product of the angular frequency (ω) and the amplitude of the motion.
What is the defining equation for simple harmonic motion (SHM)?
The defining equation for SHM is a = -ω²x, where a is acceleration, ω is angular frequency, and x is displacement.
What is phase difference in SHM?
Phase difference is the angle between radial lines in circular motion representations of two SHMs. It indicates how much one motion leads or lags behind the other.
What is the velocity equation for an object in SHM with phase angle included?
v = ωx₀ cos(ωt + ϕ), where v is velocity, ω is angular frequency, x₀ the amplitude, t the time, and ϕ the phase angle.
How do you calculate the phase angle (ϕ) if one oscillation is 1/8 of a period ahead or behind another oscillation?
The phase angle ϕ can be calculated using the proportion of the period completed: ϕ = (1/8) * 2π = π/4 radians.
How do you calculate the period of motion in SHM when given the angular frequency ω?
T = 2π/ω, where T is the period of motion and ω is the angular frequency.
How do you calculate the maximum velocity of a particle in SHM?
Maximum velocity in SHM is ωx₀, with ω as angular frequency and x₀ as amplitude.
How do you calculate the acceleration of a particle in SHM?
The acceleration is given by a = -ω²x, where ω is the angular frequency and x is the displacement.
What does the kinetic equation for simple harmonic motion involve?
The kinetic equation for simple harmonic motion involves the expression (1/2)mv^2, with m representing mass and v as the velocity, given by v = ±ω√(A^2 – x^2), where ω is the angular frequency, A is the amplitude, and x is the displacement from equilibrium.
When are the kinetic and potential energies equal in simple harmonic motion?
In simple harmonic motion, the kinetic and potential energies are equal when the displacement of the object is closer to the amplitude x0 than the equilibrium point (not exactly halfway).
Who is credited with the observation that the time period of a simple pendulum does not depend on its amplitude (for small amplitudes)?
Galileo is credited with this observation.
How did Galileo discover that a pendulum's period is independent of amplitude?
Galileo observed a chandelier at Pisa Cathedral and timed the swings with his pulse. He found that the swing count over a set pulse count remained constant, showing that the pendulum's period was independent of swing amplitude.
How did pendulum experiments advance scientific understanding of time measurement?
Pendulum experiments paved the way for precise time measurement in scientific studies, leading to developments in mechanics and reinforcing the role of experimental data in advancing scientific knowledge.
What is a limitation of a simple pendulum in SHM?
A simple pendulum approximates SHM and deviates at large swing amplitudes.
How can a timepiece be modified to achieve isochronous oscillations?
To achieve isochronous oscillations in a timepiece, adjustments can be made to the timepiece's mechanism to ensure equal oscillation periods regardless of swing amplitude. This is often done using a governing device.
What is the term for the position a system adopts when at rest?
Equilibrium position.
What is the term for the time taken to complete one cycle of an oscillation?
Time period (T).
What is the relationship between the frequency (f) of oscillation and the time period (T)?
The frequency (f) is the reciprocal of the time period (T). Therefore, f = 1/T. This means that the frequency is the number of oscillations per unit time, and the time period is the time for one complete oscillation.
What is the unit for frequency?
Hertz (Hz), which is the same as s−1.
What device is used to monitor the mass's position in a mass-spring system experiment?
A common device for tracking the position of the mass in a mass-spring oscillator is an ultrasound motion sensor.
What is the effect of gravity on an object in free fall?
The object accelerates downwards at approximately 9.8 m/s².
What happens when a projectile is launched at an angle?
The initial velocity has both horizontal and vertical components, affecting the range and maximum height.
What is the effect of increasing the launch angle (below 45 degrees) on the range of a projectile?
The range increases.