STATEMENT-1 `:` The energy is increased because the amplitude is increased .
and
STATEMENT-2 `:` The amplitude is increased because energy is increased.

Answer

To analyze the given statements, we need to understand the relationship between energy and amplitude in oscillatory motion.

### Step 1: Understand the relationship between energy and amplitude
In oscillatory systems, such as a pendulum or a mass-spring system, the total mechanical energy (E) is related to the amplitude (A) of the oscillation. The formula for the total energy in terms of amplitude is given by:

\[ E = \frac{1}{2} k A^2 \]

where \( k \) is the spring constant for a spring system or a similar constant for other systems.

### Step 2: Analyze Statement 1
**Statement 1:** "The energy is increased because the amplitude is increased."

From the formula, we see that if the amplitude \( A \) increases, the total energy \( E \) also increases, since energy is proportional to the square of the amplitude. Therefore, this statement is **true**.

### Step 3: Analyze Statement 2
**Statement 2:** "The amplitude is increased because energy is increased."

If we consider that energy can be supplied to the system (for example, by pushing a pendulum or stretching a spring), increasing the energy will indeed lead to an increase in amplitude. Thus, this statement is also **true**.

### Conclusion
Both statements are true. The relationship between energy and amplitude is such that an increase in one leads to an increase in the other.

### Final Answer
Both Statement 1 and Statement 2 are true.

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