What is the formula for amplitude in simple harmonic motion?
x(t)=Acos(ωt+φ). x ( t ) = A cos ( ω t + φ ) . This is the generalized equation for SHM where t is the time measured in seconds, ω is the angular frequency with units of inverse seconds, A is the amplitude measured in meters or centimeters, and φ is the phase shift measured in radians ((Figure)).
What happens to the time period of a simple pendulum if the length is doubled?
Time period is directly proportional to the length…. So if length is doubled the time period is doubled. Time period does not depend on the mass of the object suspended ….. So it will have no effect on its value.
What will be the time period of second’s pendulum if its length is doubled ? (Ans. 2.828 s) 1.
What is the time period of a seconds pendulum?
two seconds
Why the amplitude of the vibrating pendulum should be small?
When amplitude of the vibrating pendulum is small then angular displacement of the bob used in simple pendulum is small. Since F is directed towards mean position, therefore the motion of the bob of simple pendulum will be SHM if θ is small.
Does period of pendulum depend on amplitude?
In fact, though, the pendulum is not quite a simple harmonic oscillator: the period does depend on the amplitude, but provided the angular amplitude is kept small, this is a small effect. The mass cancels between the two sides, pendulums of different masses having the same length behave identically.
Why does frequency depend on mass?
In this case the Characteristic or the Natural Frequency of the system Does depend on the mass. In this case the restoring force constant i.e mg itself depends on mass and in this case it turns out that the ratio of restoring force constant to mass is a constant. Hence the natural frequency Does not depend on mass.
An object’s natural frequency is the frequency or rate that it vibrates naturally when disturbed. Objects can possess more than one natural frequency and we typically use harmonic oscillators as a tool for modeling the natural frequency of a particular object.
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