Oscillating Systems Flashcards
Describe the motion of a pendulum
Acceleration in a pendulum is determined by newtons second law. Acceleration is the gravitational constant of 9.81m/s² × the sine of the θ to direction of motion. When the pendulum is perpendicular to gravity sin = 1 and there will be maximum acceleration. When the pendulum is at the lowest point and thus parallel to gravity sine = 0.
Explain simple harmonic motion
SHM is a type of oscillatory motion where the acceleration is directly proportional to the degree of (linear or angular) displacement and in the opposite direction. For example the strength of acceleration of a spring is determined by the K value and how far it is displaced from its neutral position. The acceleration is also in the opposite direction to the direction of its displacement.
Explain the calculations for frequency and period of pendulum motion
Because all objects (with low air resistance) have the same gravitational acceleration of 9.81 m/s² the mass of a pendulum bob does not affect the speed of the period. It is the length of the pendulum that slows the movement. The formula for time period is 2π × √(L/g). The formula for frequency is (2π × √(L/g))⁻¹
Explain forcing and damping
No oscillatory motion continues indefinitely because there is always some type of friction in the system (e.g air resistance) that means every oscillation is smaller than the last. With artificial dampers that add additional friction the motion is reduced fast still. For example a mass on a string moving in liquid will stop oscillating far quicker than a mass in the air. This first is called light damping and the later heavy damping.
Why is it necessary to intentionally dampen vibrations.
Vibrations can work machine parts loose and affect the accuracy of instruments.
Explain forced vibration
When a vibration is subject to damping due to external vibrations the internal vibration will start to vibrate at the same frequency as the external. This is called forced vibration.
Explain the concept of resonance
When the external driving force vibrates at the same frequency as the internal force we say that resonance occurs. For example pushing a pendulum in time with its natural movement. The external force will thus amplify the natural vibration increasing its amplitude. If the amplitude reaches a certain point the system will fail. Thus resonance is a problem to be avoided in most systems.
Define oscillation
Oscillation is movement to and from extreme limits, e.g pendulum swinging, vibrations, car suspension absorbing shock.
