Damp oscillation
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The document discusses a damped mass-spring oscillator that loses 4% of its energy each cycle. The period is 2.0 seconds, the mass is 0.20 kg, and the initial amplitude is 0.30m. Using these values and the equation A(t)=Ae^(-bt/2m), the damping constant b is calculated to be 0.0124 kg/s. It also calculates that it would take approximately 6.54 cycles for the amplitude to reduce to 0.20m. Decreasing the damping constant would increase the number of cycles needed to reduce the amplitude as it weakens the drag force.
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2014 st josephs geelong physics lecture
This document contains a summary of past VCE physics exam questions from 2010-2013. Key points include:
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2) Sample questions were provided on topics like springs, momentum, transformers, semiconductors, and astronomy. Detailed explanations of correct answers were given.
3) Tips were provided on how to approach particular question types, like using diagrams and considering change in magnetic flux for transformer questions. Common errors were also noted.
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The document discusses the response of single degree of freedom (SDOF) systems to undamped and damped free vibration. It provides the equations of motion and solutions for undamped free vibration. It discusses the effects of initial conditions and how to determine the natural frequency, period and equivalent static force. The document also discusses viscously damped systems and provides solutions for underdamped, critically damped and overdamped systems. It provides typical damping ratios for different structural materials and systems. Example problems are also included.
Physicalquantities
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2) Standard SI units are provided for different base physical quantities. Prefixes are also introduced to denote multiples and submultiples of units.
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2. The period T of a spring is the time for one complete oscillation, related to spring constant k and mass m by T=2π√(m/k). Frequency f is the number of oscillations per second, with f=1/T.
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Physics of nuclear medicine.pptx
This document provides information about physics concepts in nuclear medicine including radioactivity, radioisotopes, half-life, and activity calculations. It defines alpha, beta, and gamma radiation emissions and their properties. It discusses isotopes, radioisotopes, and radionuclides. Formulas are provided for calculating activity, decay constant, and half-life. Examples are given for calculating mass of radioisotopes and activity remaining after a given time based on the half-life.
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2. The document then covered topics like equilibrium, restoring forces, characteristics of periodic motion, and the mathematics of simple harmonic oscillators.
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Lo2: Damped Oscillations
1. Goose wants to know the mass of his pencil box without a scale by using a rubber band, ruler, timer and laptop. He attaches the rubber band to a tree and pencil box, stretching it from 1-6 cm. After releasing it when stretched to 14 cm, it oscillates down to 11 cm over 3 oscillations.
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3. For a string fixed at both ends, standing waves can form with wavelengths of 2L/m, where L is the string length and m is a positive integer. The lowest frequency is called the fundamental frequency. Higher integer multiples of this frequency are the harmonics.
Similar to Damp oscillation (20)
Fourier Series for Continuous Time & Discrete Time Signals
Fourier Series for Continuous Time & Discrete Time Signals
Damp oscillation
- 2. •Supposed that a damped mass-spring oscillator loses 4% of its energy during each cycle. If the period is 2.0 s, the mass is 0.20 kg, and the initial amplitude is 0.30m Question 1: What is the value of the damping constant
- 3. Explanation • Damped oscillator oscillates at a lower frequency, and the damped amplitude decreases over time. We combined the amplitude and a exponential term to express a relationship between amplitude and time passes. • Key equation: A(t)=Ae^(-bt/2m)
- 4. Calculation:• the initial amplitude is 0.3 • Amplitude of the oscillator after 1 oscillation: 0.3*(1- 4%)=0.288 • We know that T=2.0, and mass is= 0.20 • We can then plug in all the values into the equation: A(t)=Ae^(-b/m) 0.3*e^(-bt/2m)=0.288 e^(-bt/2m)=0.94 ln94=-bt/2m b=-2m/t*ln(0.95) b=-0.20*2/2.0*ln(0.94) b=0.0124kg/s
- 5. Question 2: How many cycles elapsed before the amplitude reduces to 0.20m? • We can also apply the key equation A(t)=Ae^(-bt/2m) in this question. • We can use this equation to calculate the time elapsed. Calculation of t: A(t)=Ae^(-bt/(2m)) A(t)/A=e^(-bt/(2m)) ln(0.2/0.3)=-bt/(2m) ln(3/2)=bt/(2m) t=ln(2/3)*2m/b t=2*0.20/(0.0124)*ln(2/3) t=13.08s
- 6. Number of cycle=time/period •t/T=13.08/2.0 •t/T=6.54 •Therefore, around 6.54cycles elapsed before amplitude reaches to 0.20
- 7. Extended Question(no calculation is required): • 1. Would it take the same number of circles to reduce the amplitude from 0.2 to 0.1? • 2. How would the number of circles change if you decrease the damping constant.
- 8. Answers: • 1. No. According to the equation A(t)=Ae^(-bt/2m), the amplitude decreases exponentially not linear. So it takes different amount of time to reduce the amplitude from 0.2 to 0.1. • 2. Number of circles will increase. Damping constant measures the strength of the drag force. So as you decreases the constant, the drag force decreases. Number of circles oscillate increases. Also, you can observe the relationship from the equation A(t)=Ae^(-bt/2m) that t and k are inversely proportional.