force is required to stretch it a certain length than you would need to stretch a less stiff spring the same length.
How do you find the amplitude of oscillation?
- The angular frequency ω, period T, and frequency f of a simple harmonic oscillator are given by ω=√km, T = 2π√mk, and f = 12π√km, where m is the mass of the system and k is the force constant.
- if one increases the mass of a simple harmonic oscillator (and keeps everything else the same) the frequency of oscillation must decrease. This means that the oscillator will move more slowly. On the other hand if one increases the spring constant K the frequency will increase.
- So, recapping, the period of a mass on a spring does not depend on the amplitude. You can change the amplitude, but it will not affect how long it takes this mass to go through a whole cycle.
- x(t) = A cos(ωt + φ). A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction.
0.43622 seconds
0.9158 foot
-4.43 ffot/sec
we first find the period of oscillation
= 2π√w/gk
= 2π√4000/32x2600
= 2π√0.00481
= 2π0.0694
= 0.43622
b. we find the angular velocity
2π/T
= 2π/0.43622
= 14.41 rad/sec
we find displacement
rom the calculation in the attachment
Ф = -144.1
initial condition
1*cos(-144.1 rad)
= 0.9158 foot
initial velocity of the car
= (-1)(14.41)sin(ω(0)-144.1)
= -4.44 foot/sec
To learn more about Initial conditions refer to:
https://brainly.com/question/23731139
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