Question

An impulsive force gives an initial velocity of =1.0 m/s to the mass in the
unstretched spring position. What is the amplitude of motion? Give x as a
function of time t for the oscillating mass. Given m= 3 kg and k =1200 N/m

Answer 1

Given

• Initial Velocity = -1 m/s
• m = 3 kg
• k = 1200 N/m

To Find

• Amplitude of motion

Solution

● ω = √{k/m}

● Amplitude = (vₘₐₓ)/ω

✭ Angular Velocity :

→ ω = √{k/m}

→ ω = √{1200/3}

→ ω = √400

→ ω = 20 rad/s

✭ Amplitude :

→ Amplitude = (vₘₐₓ)/ω

→ Amplitude = 1/20

→ Amplitude = 5 m

Answer 2

Answer:-

$\small \bf \underline{Given:}$

★★ Initial velocity = -1m/s

★★ m = 3kg

★★ k = 1200N/m

$\small \bf \underline{To \: find:}$

We need to find the amplitude of the motion

$\small \bf \underline{Solution:}$

»Angular velocity :-

$\bf{ \omega} = \sqrt{ \frac{k}{m} }$

$\bf = > { \omega} = \sqrt{ \frac{1200}{3} }$

$\bf = > { \omega} = \sqrt{400}$

$\bf = > { \omega} = 20 \: rad/s$

»Amplitude :-

$\small \bf \: Amplitude \: = \: \frac{V_{max}}{{ \omega}}$

$\small \bf \: Amplitude \: = \: \frac{1}{20}$

$\small \bf \: Amplitude \: = \: 5cm$

Answer: The amplitude is 5cm.

@BengaliBeauty

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