Answer :
a) The instant that the mass passes through the position where the spring is unstretched, what can be said about its instantaneous acceleration being zero,
c) The instant that the spring is compressed the most, what can be said about the magnitude of its instantaneous velocity of Speed is Zero
a) the equation that governs the simple harmonic motion is
x = A cos (wt +φφ)
Where A is the amplitude of the movement, w is the angular velocity, and φ the initial phase determined by the initial condition
Body acceleration is
a = d²x / dt²
Let's look for the derivatives
dx / dt = - A w sin (wt + φ)
a = d²x / dt² = - A w² cos (wt + φ)
In the instant when it is not stretched x = 0
As the spring is released at maximum elongation, φ = 0
0 = A cos wt
Cos wt = 0 wt = π / 2
Acceleration is valid for this angle
a = -A w² cos π/2 = 0
Acceleration is zero
b)
c) When the spring is compressed x = A
Speed is
v = dx / dt
v = - A w sin wt
We look for time
A = A cos wt
cos wt = 1 wt = 0, π
For this time the speedy vouchers
v = -A w sin 0 = 0
Speed is cero
Harmonic movement refers to the movement of an oscillating mass studies when the restoring pressure is proportional to the displacement, however in contrary directions. Harmonic motion is periodic and may be represented with the aid of a sine wave with regular frequency and amplitude. An example of that is a weight bouncing on a spring. The motion is called harmonic due to the fact musical contraptions make such vibrations that during flip cause corresponding sound waves in the air.
it is a sort of periodic motion with extreme points. simple harmonic motion is an oscillatory motion wherein the particle's acceleration and force are without delay proportional to its displacement from the mean region at every factor. it's miles a special case of oscillatory movement.
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