1. A spring-mass system oscillat3es with a period of 6.4s. If the mass attached

ID: 1475934 • Letter: 1

Question

1. A spring-mass system oscillat3es with a period of 6.4s. If the mass attached to the spring is 0.16kg, what is the spring constant?

2. A simple pendulum oscillates with a period of 1.2s. If the length of the pendulum is doubled, what will be the period of the pendulum?

3. The displacement of a simple harmonic motion is given by x=1.2 cos (2t + /3) in meters. what is the maximum speed of the motion?

4. The maximum speed and the maximum acceleration of a simple pendulum is 1.2m/s and 1.8m/s^2 respectively. What is the ampllitude of the pendulum.

here,

period , P = 6.4 s

the mass attached , m = 0.16 kg

let the spring constant be k

P = 2*pi*sqrt(m/k)

6.4 = 2*pi*sqrt( 0.16/k)

k = 0.154 N/m

period of pendulam , T = 1.2 s

length of pendulam be l

when l' = 2 *l

T = 2*pi*sqrt(l'/g)

T = sqrt(2) * 2*pi*sqrt(l/g)

T = 1.7 s

the time period is 1.7 s

amplitude , A = 1.2 m

w = 2

maximum velocity , v = A*w

v = 2*1.2

v = 2.4 m/s

the maximum velocity is 2.4 m/s

maxuimum velocity , v = 1.2 m/s

A*w = 1.2

maximum accelration , a = 1.8 m/s^2

A*w^2 = 1.8

1.2*w = 1.8

w = 1.5 rad/s

A*w = 1.2

A = 0.8 m

the amplitude of the pendulam is 0.8 m

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