A block with mass 0.55 kg on a frictionless surface is attached to a spring with spring constant 43 N/m. The block is pulled from the equilibrium position and released. What is the period of the system?

period = 2*pi*sqrt(m/k)= 0.71 seconds

where k is the spring constant and m is the mass.

To find the period of the system, we need to use Hooke's Law and the equation for the period of a mass-spring system.

Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The equation for Hooke's Law is:

F = -kx

Where:
F is the force exerted by the spring (in Newtons),
k is the spring constant (in N/m),
x is the displacement from the equilibrium position (in meters).

In this problem, the block is pulled from the equilibrium position and released. At any point in time, the force exerted by the spring is equal to the force pulling the block back towards equilibrium, which is given by Hooke's Law:

F = -kx

We know that the force exerted by the spring is equal to the mass of the block multiplied by its acceleration. Using Newton's second law (F = ma), we can rewrite the equation as:

m * a = -k * x

Rearranging the equation, we have:

a = -(k / m) * x

Since acceleration (a) is the second derivative of displacement (x) with respect to time (t), we have:

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

This is a second-order linear differential equation. The general solution to this equation is:

x(t) = A * sin(ωt + φ)

Where:
x(t) is the displacement of the block as a function of time,
A is the amplitude of the oscillations,
ω is the angular frequency of the system (related to the period via T = 2π/ω),
φ is the phase constant.

Comparing this equation with the general solution, we can see that the angular frequency ω is equal to √(k/m). Therefore, the period of the system T is given by:

T = 2π / ω = 2π √(m/k)

Substituting the given values:
m = 0.55 kg (mass of the block), and
k = 43 N/m (spring constant),

T = 2π √(0.55 kg / 43 N/m)

Calculating this expression will give us the period of the system.