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Individual tasks for PROBLEM 3.3.
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DAMPED HARMONIC OSCILLATIONS.
In accordance with your variant to solve one of the following problems listed below (The number of problem statement and all necessary input data are reduced in the table 3.3).
1 Load of mass of m, suspended on the spring with stiffness of k, oscillate in viscous medium with drag coefficient of r. The equation of oscillations of load has view x (t) = А 0 ·e- β t· cosω t. Logarithmic decay decrement of oscillations is δ.
a) By the values of quantities, given in the table 3.3, find necessary parameters and write down the equation of vibrations with numerical coefficients.
b) Find the system quality factor.
c) Find the quantity, which is indicated in the last column of table.
2 The oscillation circuit consists of capacitor with capacity of С, coil of inductance of L and resistor of resistance of R. Current in circuit changes by law i (t) = I 0 ·e– β t · sinω t. Logarithmic decay decrement of oscillations is δ.
a) By the values of quantities, given in the table 3.3, find necessary parameters and write down the equation of current’s oscillations with numerical coefficients.
b) Find the system quality factor.
c) Find the quantity, which is indicated in the last column of table.
TABLE OF TASK VARIANTS
Table 3.3
| Variant | Statement | k, N/m | r, kg/s | m, g | А, cm | С, mF | L, mH | R, Ω | I 0, mА | β, s–1 | ω, rad/s | δ | Find |
| – | – | – | – | – | – | – | δ | ||||||
| – | – | – | – | – | – | – | 0, 9 | L | |||||
| – | – | – | – | – | – | – | 1, 2 | С | |||||
| – | – | – | – | – | – | – | 104 | L | |||||
| – | 0, 5 | – | – | – | – | – | – | k | |||||
| – | – | – | – | – | – | – | 1, 7 | С | |||||
| – | – | – | – | – | – | – | 1, 1 | r | |||||
| – | – | – | – | – | – | – | 1, 8 | L | |||||
| – | – | – | – | – | – | – | 1, 5 | С | |||||
| – | – | – | – | – | – | – | 1, 6 | k | |||||
| – | – | – | – | 0, 5 | – | – | – | δ | |||||
| – | – | – | – | – | – | – | R | ||||||
| 1, 6 | – | – | – | – | – | – | – | δ | |||||
| – | – | – | – | – | – | – | 1, 9 | С | |||||
| – | – | – | – | – | – | – | 1, 8 | r | |||||
| – | – | – | – | – | – | 5·103 | – | δ | |||||
| – | 1, 2 | – | – | – | – | – | – | 1, 5 | k | ||||
| – | – | – | – | – | – | – | 1, 6 | R | |||||
| – | – | – | – | – | – | – | 1, 2 | k | |||||
| – | – | – | – | – | – | – | 2·104 | 1, 5 | L | ||||
| – | – | – | – | – | – | – | 1, 4 | С | |||||
| – | – | – | – | – | – | – | 1, 4 | r | |||||
| – | – | – | – | – | – | – | 1, 3 | R | |||||
| 0, 8 | – | – | – | – | – | – | – | δ | |||||
| – | – | – | – | 0, 2 | – | – | – | 1, 1 | L | ||||
| – | – | – | – | – | – | – | 1, 3 | k | |||||
| – | – | – | – | – | – | – | 1, 1 | С | |||||
| – | 1, 1 | – | – | – | – | – | – | 1, 4 | k | ||||
| – | – | – | – | – | – | – | δ | ||||||
| – | – | – | – | – | – | – | 1, 2 | r |
Problem 3.4.
DRIVEN HARMONIC OSCILLATIONS
MAIN CONCEPTS
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