I have a question to the last part in the green box, how do I apply the same con

Question

I have a question to the last part in the green box, how do I apply the same concept from the block and spring to find the frequency of the pendulum? thanks!

Example 28.2 The Quantized Oscillator ProblemA3.0kg block is attached to a massless spring of force constantk=23N/m. The spring is stretched 0.40 m from its equilibrium position and released.

Find the total energy and frequency of oscillation according to classical calculations.

Assuming that the energy is quantized, find the quantum numbernfor the system.

How much energy is carried away when the oscillator makes a transition to the next lowest quantum state? StrategyBecause of our study of oscillating blocks in Chapter 12, this problem is easy to conceptualize. The phrase "according to classical calculations" tells us that we should categorize this part of the problem as a classical analysis of the oscillator.
Solution To analyze the problem, we know that the total energy of a simple harmonic oscillator having an amplitude A iskA2(Eq. 12.21). Therefore, we have the following. J
The frequency of oscillation is the following, given by Equation 12.14. Hz
This part of the problem is categorized as a quantum analysis of the oscillator. To analyze the problem, we note that the energy of the oscillator is quantized according to Equation 28.2. Therefore, we have the following. En= nhf = n(6.6310-34J

Explanation / Answer

Time period of the pendulum is given as

T = 2 * (L/g)

L----length of the string of the pendulum

g----acceleration due to gravity = 9.8 m/sec^2

T = 2 * (1.7/9.8) = 2.62 sec

frequency = 1/T = 0.382 Hz

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.