Question

A vertical spring mass system has a mass of 0.5 kg and an initial deflection of 0.2 cm. Find the spring stiffness and the natural frequency of the system

Answer 1

Answer:

Introduction

All systems possessing mass and elasticity are capable of free vibration, or

vibration that takes place in the absence of external excitation. Of primary interest

for such a system is its natural frequency of vibration.

The basic vibration model of a simple oscillatory system consists of a mass, a

massless spring, and a damper.

If damping in moderate amounts has little influence on the natural frequency, it

may be neglected. The system can then be considered to be conservative.

An undamped spring-mass system is the simplest free vibration system. It has

one DOF.

2. Equation of Motion

Answer 2

Given:

Vertical spring system

Mass of the system, m = 0.5 kg

initial deflection of the spring, x = 0.2 cm

Formula Used:

Spring force, $F=kx$

where, k is the spring stiffness is constant and deflection of the spring.

$\omega=\sqrt \frac{k}{m}\\f=\frac{1}{2\pi}\sqrt \frac{k}{m}$

Calculations:

For vertical spring system

$kx=mg\\k=\frac{mg}{x}\\k=\frac{0.5\times 9.8}{0.002} = 2450 N/m$

$f=\frac{1}{2\pi}\sqrt \frac{k}{m}\\f=\frac{1}{2\pi}\sqrt \frac{2450}{0.5} =11.15 Hz$

Learn more about: Spring-mass system

brainly.in/question/13454479

#learnwithbrainly