A block on a spring moves in SHM with amplitude 0.23 m and period 3.8 s. The mass of the block is 2.1 kg. What is the total energy of the system?

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To determine the total energy of the system, we can use the formula for the total energy of an object undergoing Simple Harmonic Motion (SHM).

The formula for the total energy (E) of an object in SHM is given by:

E = (1/2) * k * A^2

Where:
- E is the total energy
- k is the spring constant
- A is the amplitude

To find the spring constant (k), we can use the formula:

k = (2 * π / T)^2 * m

Where:
- T is the period of the motion
- m is the mass

Let's calculate it step by step:

1. Calculate the spring constant (k):
k = (2 * π / T)^2 * m

Given:
T = 3.8 s (period)
m = 2.1 kg (mass)

k = (2 * π / 3.8)^2 * 2.1
k ≈ 14.22 N/m

2. Calculate the amplitude (A):
Given:
A = 0.23 m (amplitude)

3. Calculate the total energy (E):
E = (1/2) * k * A^2

E = (1/2) * 14.22 * 0.23^2
E ≈ 0.189 J (joules)

Therefore, the total energy of the system is approximately 0.189 joules.