One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to the x-axis. A block of mass m = 1 kg is attached to the free end of the spring and it is performing SHM. Equation of position of the block in coordinate system shown in figure is x = 10 + 3sin(10t), where t is in seconds and x in centimetres. The force constant of spring is 4n². Where n = _____.
Physics · Mixed Chapter
JEE Mains

Question

One end of an ideal spring is fixed to a wall at origin O and axis of spring is parallel to the x-axis. A block of mass m = 1 kg is attached to the free end of the spring and it is performing SHM. Equation of position of the block in coordinate system shown in figure is x = 10 + 3sin(10t), where t is in seconds and x in centimetres. The force constant of spring is 4n². Where n = _____.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The sinusoidal displacement about the equilibrium position is 3sin(10t) cm, so angular frequency is ω=10 rad s⁻¹. Step 2: For mass-spring SHM, ω²=k/m. With m=1 kg, k=mω²=100 N m⁻¹. Step 3: Given k=4n², set 4n²=100, so n²=25. Step 4: Positive n=5.