9 Lab 9 Simple Harmonic Motion SHM l

實驗 9：簡諧運動 Lab. 9 : Simple Harmonic Motion (SHM) 實驗目的：研究滑車在滑軌上，因彈簧的恢復力而做 的簡諧運動 l測量彈簧的靜態彈性係數 ks 和動態彈性係數kd l. SHM之週期T與運動物體質量m的關係 l. SHM之週期與彈性係數 k 的關係 Object: Observe the simple harmonic motion of the object applied by the restoring force of a spring and measure l. Both static and dynamic spring constants of the spring, ks & kd l. Relation of the SHM period T and mass of the motional object Physics. NTHU l. Relation of the SHM period T and the spring constant k MFTai-戴明鳳

Simple harmonic motion - SHM Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. l The motion is sinusoidal in time and demonstrates a single resonant frequency. l Undamped spring-mass SHM Damped Physics. NTHU spring-mass SHM MFTai-戴明鳳 Countsey: http: //en. wikipedia. org/wiki/Simple_harmonic_motion

Hook’s Law & Harmonic Oscillating System An undamped springmass system undergoes simple harmonic motion. Physics. NTHU MFTai-戴明鳳

Various Harmonic Oscillating System An undamped spring-mass system undergoes simple harmonic motion. Physics. NTHU MFTai-戴明鳳

Various SHM Systems l Two SHM Examples l SHM of Simple pendulum l Circular SHM l Coupled SHM l Damped SHM l Driven SHM Web site: Acoustics and Vibration Animations Physics. NTHU http: //www. kettering. edu/~drussell/Demos. html MFTai-戴明鳳

Mass-Spring Systems without Damping Mass-Spring Systems with Damping Forced Harmonic Oscillator Physics. NTHU MFTai-戴明鳳

Physics. NTHU MFTai-戴明鳳

Damped Harmonic Oscillation Physics. NTHU MFTai-戴明鳳

Friction-Constant Damping Physics. NTHU MFTai-戴明鳳

Physics. NTHU MFTai-戴明鳳

Period Amplitude Velocitydependent damping Increase Exponential decay Constant damping No change Linear decay Physics. NTHU MFTai-戴明鳳

Coupled Oscillators -Daniel A. Russell, Kettering University l Two mass-spring oscillators are coupled together by a stretchy cord. Physics. NTHU MFTai-戴明鳳