What is the maximum displacement in SHM?
Maximum displacement is the amplitude A. The angular frequency ω , period T, and frequency f of a simple harmonic oscillator are given by ω=√km ω = k m , T=2π√mk,andf=12π√km T = 2 π m k , and f = 1 2 π k m , where m is the mass of the system and k is the force constant.
How do you find maximum displacement in trigonometry?
d = A sin (kt + c). Remember: The amplitude of an object is its maximum displacement from the zero point. The period is the time it takes to complete one cycle. The frequency is the number of cycles per unit of time.
Does the period depend on the mass?
The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. With the assumption of small angles, the frequency and period of the pendulum are independent of the initial angular displacement amplitude. A pendulum will have the same period regardless of its initial angle.
Why does period not depend on mass?
The period of oscillation of a simple pendulum does not depend on the mass of the bob. Since the mass factors into both the cause of changing motion and the resistance to changing motion, it cancels out. For a mass-spring system, the mass still affects the inertia, but it does not cause the force.
Why does mass not affect period?
The mass of the bob does not affect the period of a pendulum because (as Galileo discovered and Newton explained), the mass of the bob is being accelerated toward the ground at a constant rate — the gravitational constant, g.
Why does period depend on length?
The longer the length of string, the farther the pendulum falls; and therefore, the longer the period, or back and forth swing of the pendulum. The greater the amplitude, or angle, the farther the pendulum falls; and therefore, the longer the period.)
Does amplitude increase with mass?
Increasing the amplitude means the mass travels more distance for one cycle. The increase in force proportionally increases the acceleration of the mass, so the mass moves through a greater distance in the same amount of time. Thus, increasing the amplitude has no net effect on the period of the oscillation.
How does gravity affect oscillation?
For gravity, the inverse relationship shows that the stronger the gravitational acceleration, the smaller the period of oscillation. For example, the period of a pendulum on Earth would be smaller compared to a pendulum of equal length on the moon.
What factors increase the speed of a pendulum?
Which factors increase the maximum velocity of a pendulum? Explanation: Both the length of the pendulum’s string and the angle of displacement affect the maximum velocity of the pendulum.
Does a pendulum swing faster with more weight?
When you add a weight to the bottom of the pendulum on the right, you make it heavier. When you add a weight to the middle of the other pendulum, however, you effectively make it shorter. Shorter pendulums swing faster than longer ones do, so the pendulum on the left swings faster than the pendulum on the right.
How do I make my pendulum swing slower?
The swing rate, or frequency, of the pendulum is determined by its length. The longer the pendulum, whether it is a string, metal rod or wire, the slower the pendulum swings.