Laboratory work № 41

SPRING PENDULUM

Purpose of the work is to study dependence of period of oscillations on mass for a spring pendulum.

Task: to define acceleration offree falling; experimentally to check up the theoretical formula of period of the spring pendulum.

Theory

Oscillations of a spring pendulum are acted upon by the elastic force

, (2.1)

where x is a deviation from state of stable equilibrium, k is a rigidity of the spring. The period of oscillations is

, (2.2)

where m is mass of the body fixed on the spring.

Spring pendulum (fig.2.1) it a body is suspended on a spring. At the leadingout of it from position of equilibrium of x_o on distance of x there is force of elasticity F, which by Hook`s law is evened F = -kx, where k is rigidity of spring. This force gives the acceleration

, or . (2.3)

Equation (2.1) can be write down in such a way

. (2.4)

Designating , get . (2.5)

Equation (2.3) is named differential equation of undamped free harmonic oscillations. The decision of this equation is a harmonic function

, or (2.6)

what sets the coordinate of x load in any moment of time t.

Will consider descriptions of harmonic oscillations. Amplitude of A_o is most deviation of point from position of equilibrium

Cyclic frequency of oscillations – (2.7)

it is an amount of oscillations for 2π seconds.

Period of oscillations – (2.8)

it is time of one full-oscillate, or time for which the phase of oscillation changes on 2π.

Frequency of oscillations – (2.9)

it is an amount of oscillations for 1 second.