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# 221 Lab 4 Simple Harmonic Motion I. to a simple harmonic.

II. Simple Pendulum The motion of a pendulum can be treated as simple harmonic if: 1. there is no friction and 2. if the displacement of the mass m from the equilibrium position is small, ≤ 15o The period of a pendulum undergoing simple harmonic motion is described by: T = 2 § Å Ú.

Simple Harmonic Motion–Pendulum Mechanics: simple harmonic motion, pendulum GLX setup file: pendulum Qty Equipment and Materials Part Number 1 PASPORT Xplorer GLX PS-2002 1 PASPORT Motion Sensor PS-2103 1 Universal Table Clamp ME-9376B 1 Rod, 45 cm ME-8736 1 Pendulum Clamp SE-9443 1 Meter Stick SE-8695 1 Balance SE-8723.
Although commonly used in the teaching of simple harmonic motion a swinging pendulum does not perfectly fit the conditions for SHM. However, if we are careful, a swinging pendulum moves in very nearly simple harmonic motion. The angle of swing must be small and the mass must be large compared to the mass of the string/wire. 58 Experiment 11: Simple Harmonic Motion Advance Reading Text: Simple harmonic motion, oscillations, wave-length, frequency, period, Hooke’s Law. Lab Manual: Appendix B Objective To investigate simple harmonic motion using a simple pendulum and an oscillating spring; to determine the spring constant of a spring. Theory Periodic motion is.

The movement of a pendulum is called simple harmonic motion: when moved from a starting position, the pendulum feels a restoring force proportional to how far it’s been moved. Put another way, it always wants go back to where it started. Pendulums move by constantly changing energy from one form to. Simple harmonic motion is the kind of vibratory motion in which the body moves back and forth about its mean position. The motion of the swing, hand of the clock and mass-spring system are some simple harmonic motion examples. SHM in a Pendulum. The motion of a simple pendulum is very close to Simple Harmonic Motion SHM. SHM results whenever a restoring force is proportional to the displacement, a relationship often known as Hooke’s Law when applied to springs. A simple pendulum consists of a mass m hanging from a string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion. By applying Newton's secont law for rotational systems, the equation of motion for the pendulum may be obtained, and rearranged as. For a simple pendulum you can describe it using equations of motion of a simple harmonic oscillator. The equation of motion works well for smaller values of angle and amplitude, the maximum angle, because the simple pendulum model relies on the approximation that sinθ ≈ θ for some pendulum.

Simple Pendulum. A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by. Equation 8 shows that the acceleration a of the bob is directly proportional to the displacement x and negative sign shows that it is directed towards the mean position.Hence the motion of simple pendulum is simple harmonic. Time period of simple pendulum. The acceleration of the body is given by. The above relation indicates that the force acting on the bob of the simple pendulum is directly proportional to the linear displacement which is defining a characteristic of simple harmonic motion. Hence the motion of the simple pendulum is linear S.H.M. for small amplitudes. Simple Harmonic Motion 12 SHM - Simple Pendulum If a pendulum of length l is disturbed through an angle θ1 or 3, the restoring force F component drives the bob back and through the rest 2 position g l grav acc length Period T 2S 2S θ l θ F F. If the bob of a simple pendulum is slightly displaced from its mean positon and then released, it starts oscillating in simple harmonic motion. Time period d oscillation of a simple pendulum is given as: T = 2π √l/g where, l is the effective length of the pendulum and g is the acceleration due to gravity.

## Simple Harmonic MotionPendulum Science.

Motion of a Simple Pendulum is Simple Harmonic Motion SLIM Almost a valueless body suspended by a weightless, soft and non-compressible thread from a rigid support is allowed to oscillate in simple harmonic motion from a simple pendulum.