Simple Harmonic Motion [Part-IV]

The weight (mg) and the force of the spring (Fs = -kx).

What two forces act on a block attached to a vertical spring?

When the spring force equals the block’s weight; Fs = mg

How is the equilibrium position of a vertical spring determined?

It stretches by Δy, creating a new equilibrium position.

What happens to the spring when a mass is attached?

Fnet = Fs - mg = 0

What is the condition for equilibrium in a vertical spring?

-k(-Δy) = mg => k(y0 - y1) = mg

How can equilibrium stretch be expressed mathematically?

It oscillates in SHM around the new equilibrium position.

What happens if the block is displaced from equilibrium and released?

Gravity only shifts the equilibrium; it does not change the period or frequency.

How does gravity affect SHM in a vertical spring?

Fnet = -k(y - y1)

What is the net force when the block is displaced to position y?

Because the equilibrium position can be chosen as the reference point (y = 0)

Why can we set y1 to zero?

m*((d^2)(x))/dt^2 = -kx

What is the equation of motion for a block on a vertical spring?

It is mathematically identical, only the equilibrium has changed.

How is this equation similar to the horizontal spring case?

y(t) = Acos(ωt + ϕ)

What is the solution for position in vertical spring SHM?

Velocity and acceleration follow the same sinusoidal form but with phase shifts.

What do velocity and acceleration graphs look like compared to position?

At y = A: v = 0 and acceleration is negative, pointing back toward equilibrium.

What is the initial condition if the mass starts at maximum displacement?

At the equilibrium position, when y = 0

When does acceleration become zero in vertical SHM?