The torsional spring constant of the torsional oscillator (I = 0.25 kg · m² and T = 0.45 s) has a magnitude of 48.738 newton-meters.
The torsional spring constant indicates the resistance of the spring to an external moment. The torsional spring constant (κ), in newtons per meter, can be found by means of this formula in function of the period (T), in seconds and the moment of inertia (I), in kilograms per square meter:
[tex]\kappa = \frac{4\cdot \pi^{2}\cdot I}{T^{2}}[/tex] (1)
If we know that I = 0.25 kg · m² and T = 0.45 s, then the torsional spring constant of the spring is:
[tex]\kappa = \frac{4\cdot \pi^{2}\cdot (0.25\,kg\cdot m^{2})}{(0.45\,s)^{2}}[/tex]
κ = 48.739 N · m
The torsional spring constant of the torsional oscillator (I = 0.25 kg · m² and T = 0.45 s) has a magnitude of 48.738 newton-meters. [tex]\blacksquare[/tex]
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