### Forces On Bodies Systems Involving Strings Or Springs

**Concepts to remember for “Forces On Bodies - Systems Involving Strings Or Springs”**

**Newton’s Three Laws of Motion**

**First Law:**Objects in motion stay in motion, objects at rest stay at rest, unless an**external force**acts on them.**Second Law:**Force equals mass times acceleration (**F = ma**), or force is necessary to accelerate an object of mass**m**by changing its velocity with**acceleration a**.**Third Law:**For each force or interaction that occurs, there is an equal and opposite force or interaction.

**Tension**

- The force exerted by a string in a system is called
**tension force**. - Tension force always acts
**away**from the point where the string is held, and is**equal**throughout a taut (rigid) string.

**Hooke’s Law**

- Hooke’s Law explains the relationship between the
**deformation**of an**elastic object**(like a stretched spring) and the**restoring force**it exerts. - The force required to stretch or compress the object is directly proportional to the displacement (change in length) from its original length.
- Mathematically,
**F = -kx**, where**k**is known as the**spring constant**.

**Simple Harmonic Motion (SHM)**

- SHM is a type of periodic motion where an object repeatedly moves
**back and forth**through a**fixed point**(equilibrium position) with**constant speed**. - Key features include
**period (T)**- time for one complete cycle;**frequency (f)**- number of cycles per second;**amplitude (A)**- maximum displacement from the equilibrium position. - SHM is observed in various situations like spring-mass systems, oscillating pendulums, or AC current variations.

**Resonance**

- Resonance occurs when an external periodic force has a frequency that
**matches the natural frequency**of an oscillating system. - It results in a significant increase in the amplitude of oscillations.
- Applications include tuning musical instruments and designing shock absorbers to minimize vibrations.

**Equilibrium of Forces**

- Equilibrium is the state of a body or system where the
**net force acting on it is zero**. - To be in equilibrium, the
**vector sum**of all forces acting on the object or system must be zero. - Important for understanding stability and balance in various physical situations and problem-solving.