A mass of 0.7 kg is attached to the end of a massless spring of spring constant 0.35 N/m. It is released from rest from an extended position. After 0.8 s, the speed of the mass is measured to be 1.5 m/s. What is the amplitude of oscillation?

What is the total energy (relative to the mass at rest in the unextended position) contained in this system?

To find the amplitude of oscillation, we need to use the equation:

T = 2π√(m/k)

where T is the period of the oscillation, m is the mass, and k is the spring constant.

First, let's find the period of the oscillation. We know that the speed of the mass at 0.8 s is 1.5 m/s. Using the definition of the period, we can calculate it as follows:

period = time taken / number of oscillations

Since the mass is released from rest, it will complete one full oscillation in the given time. Therefore, the period is equal to the time taken, which is 0.8 s.

Now, we can use the formula for the period to find the amplitude:

T = 2π√(m/k)

0.8 = 2π√(0.7/0.35)

0.8 = 2π√2

√2 = π

Squaring both sides, we get:

2 = π^2

Dividing both sides by π^2, we find:

2/π^2 = 1

So the amplitude of oscillation is 1.

To find the total energy of the system, we can use the formula for the potential energy of a spring:

E = 0.5kA^2

where E is the total energy, k is the spring constant, and A is the amplitude.

We can substitute the given values into the formula:

E = 0.5 * 0.35 * 1^2

E = 0.175 J

Therefore, the total energy contained in this system is 0.175 joules.